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The heavens and the stars

60 passages · search this phrase →

Often appears with: fate, destiny, and necessity · experiment, observation, and evidence · weather, storms, and the seasons · reason and the intellect · matter, motion, and cause · geography and the description of places · perception and the senses · logic, method, and demonstration · the nature and attributes of God · species, variation, and descent · religious persecution and toleration · the earth and its formation

Usually: argument (86) · curiosity (82) · skepticism (48) · detachment (40) · wonder (34) · commentary or gloss (33) · narrative (24) · description (14) · confronting death (8) · exhortation (8)

Quotable
“An atom absorbs or emits light of a frequency which is dependent on the potential of the gravitational field in which it is situated.” Albert Einstein, Relativity: The Special and General Theory · precept
“Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body.” Albert Einstein, Relativity: The Special and General Theory · insight
“There does arise, however, a strange difficulty. The interpretation of the galactic line-shift discovered by Hubble as an expansion (which can hardly be doubted from a theoretical point of view), leads to an origin of this expansion which lies “only” about 109 years ago, while physical astronomy makes it appear likely that the development of individual stars and systems of stars takes considerably longer.” Albert Einstein, Relativity: The Special and General Theory · observation
“We are now in a position to formulate more exactly the idea of Minkowski, which was only vaguely indicated in Section XVII.” Albert Einstein, Relativity: The Special and General Theory · observation
“Observing that the water charged with gelatinous particles is in an impure state, and that the luminous appearance in all common cases is produced by the agitation of the fluid in contact with the atmosphere, I am inclined to consider that the phosphorescence is the result of the decomposition of the organic particles, by which process (one is tempted almost to call it a kind of respiration) the ocean becomes purified.” Charles Darwin, The Voyage of the Beagle · insight
“There is one marine production which, from its importance, is worthy of a particular history.” Charles Darwin, The Voyage of the Beagle · observation
“And this is he whom I call the child of the good, whom the good begat in his own likeness, to be in the visible world, in relation to sight and the things of sight, what the good is in the intellectual world in relation to mind and the things of mind:” Plato, The Republic · insight
“This interview with the Djinn took place at Nakhla, probably the "Wady Mohram" of Burckhardt, midway between Mecca and Ta‹ef, when Muhammad was driven from Mecca. A.D. 620.” Muhammad (Al-Qur'an content traditionally attributed; Rodwell as translator), The Koran (Al-Qur'an) · observation
“I may be allowed to express a hope, that the endeavour will always be to make it a table of real, and not hypothetical, electro-chemical equivalents; for we shall else overrun the facts, and lose all sight and consciousness of the knowledge lying directly in our path.” Michael Faraday, Experimental Researches in Electricity, Volume 1 · precept
“He directeth the ordinance from the heaven unto the earth; then it ascendeth unto Him in a Day, whereof the measure is a thousand years of that ye reckon.” Ali, Abdullah Yusuf; Pickthall, Marmaduke William; Shakir, M. H., Three translations of the Koran (Al-Qur'an) side by · insight
“Generalising we must say this:--There may be supposed to be extended physical objects to which the idea of motion cannot be applied.” Albert Einstein, Sidelights on Relativity · insight
“But therewith the conception of the ether has again acquired an intelligible content, although this content differs widely from that of the ether of the mechanical undulatory theory of light.” Albert Einstein, Sidelights on Relativity · observation

On the Origin of Species By Means of Natural Selection primary

Charles Darwin · 1837-1859 (major composition period; published 1859)
CHAPTER I. VARIATION UNDER DOMESTICATION. > CHAPTER 14. RECAPITULATION AND CONCLUSION. (2/3)

Darwin explains how his Beagle observations of South American distribution and geology led him to propose descent with modification, published because Wallace independently reached similar conclusions, and he argues that adaptation cannot be explained by external conditions alone.

expressing my deep obligations to Dr. Hooker, who for the last fifteen years has aided me in every possible way by his large stores of knowledge and his excellent judgment. In considering the Origin of Species, it is quite conceivable that a naturalist, reflecting on the mutual affinities of organic beings, on their embryological relations, their geographical distribution, geological succession, and other such facts…

On the Origin of Species By Means of Natural Selection primary

Charles Darwin · 1837-1859 (major composition period; published 1859)
CHAPTER I. VARIATION UNDER DOMESTICATION. > CHAPTER IV. (7/30)

Darwin illustrates natural selection with imagined wolf scenarios and real differences among cats’ hunting tendencies, then describes how plants’ nectar and insects’ pollination could favor cross-fertilization and nectar traits.

his greyhounds by careful and methodical selection, or by that unconscious selection which results from each man trying to keep the best dogs without any thought of modifying the breed. Even without any change in the proportional numbers of the animals on which our wolf preyed, a cub might be born with an innate tendency to pursue certain kinds of prey. Nor can this be thought very improbable; for we often observe g…

On the Origin of Species By Means of Natural Selection primary

Charles Darwin · 1837-1859 (major composition period; published 1859)
CHAPTER I. VARIATION UNDER DOMESTICATION. > CHAPTER V. (1/24)

Darwin introduces laws of variation, rejecting “chance” as an explanation and proposing that domestication and changing conditions disturb the reproductive system, making offspring variable and sometimes producing monstrosities.

LAWS OF VARIATION. Effects of external conditions. Use and disuse, combined with natural selection; organs of flight and of vision. Acclimatisation. Correlation of growth. Compensation and economy of growth. False correlations. Multiple, rudimentary, and lowly organised structures variable. Parts developed in an unusual manner are highly variable: specific characters more variable than generic: secondary sexual char…

On the Origin of Species By Means of Natural Selection primary

Charles Darwin · 1837-1859 (major composition period; published 1859)
CHAPTER I. VARIATION UNDER DOMESTICATION. > CHAPTER VI. (7/21)

He argues that perfected specialized structures usually leave no living intermediates, but diversified transitions are possible, illustrating with birds’ altered wing uses and a hypothetical evolution from flying fish.

from disuse, indicate the natural steps by which birds have acquired their perfect power of flight; but they serve, at least, to show what diversified means of transition are possible. Seeing that a few members of such water-breathing classes as the Crustacea and Mollusca are adapted to live on the land, and seeing that we have flying birds and mammals, flying insects of the most diversified types, and formerly had …

On the Origin of Species By Means of Natural Selection primary

Charles Darwin · 1837-1859 (major composition period; published 1859)
CHAPTER I. VARIATION UNDER DOMESTICATION. > CHAPTER XIV. (16/27)

He says descent with modification likely covers whole biological classes, argues animals probably share only a few progenitors, and uses analogy plus shared biological features to infer a single primordial origin.

from those who believe in the mutability of species, on their own side they ignore the whole subject of the first appearance of species in what they consider reverent silence. It may be asked how far I extend the doctrine of the modification of species. The question is difficult to answer, because the more distinct the forms are which we may consider, by so much the arguments fall away in force. But some arguments o…

The Koran (Al-Qur'an) primary

Muhammad (Al-Qur'an content traditionally attributed; Rodwell as translator) · c. 610–632 CE (revelations compiled into the Qur'an after the prophet’s death)
Book carefully concocted from various sources, and with much extraneous aid, and published as a divine oracle, then it would seem that the author is at once open to the charge of the grossest imposture, and even of impious blasphemy. The evidence rather shews, that in all he did and wrote, Muhammad was actuated by a sincere desire to deliver his countrymen from the grossness of its debasing idolatries–that he was urged on by an intense desire to proclaim that great truth of the Unity of the Godhead which had taken full possession of his own soul–that the end to be attained justified to his mind the means he adopted in the production of his Suras–that he worked himself up into a belief that he had received a divine call–and that he was carried on by the force of circumstances, and by gradually increasing successes, to believe himself the accredited messenger of Heaven. The earnestness of those convictions which at Mecca sustained him under persecution, and which perhaps led him, at any price as it were, and by any means, not even excluding deceit and falsehood, to endeavour to rescue his countrymen from idolatry,–naturally stiffened at Medina into tyranny and unscrupulous violence. At the same time, he was probably, more or less, throughout his whole career, the victim of a certain amount of self-deception. A cataleptic13 subject from his early youth, born–according to the traditions–of a highly nervous and excitable mother, he would be peculiarly liable to morbid and fantastic hallucinations, and alternations of excitement and depression, which would win for him, in the eyes of his ignorant countrymen, the credit of being inspired. It would be easy for him to persuade himself that he was "the seal of the Prophets," > Book," "the Seven Verses of Repetition." The Muhammadans always say "Amen" (32/56)

Sura L (Kaf) responds to Meccans’ doubts about resurrection, describes creation of heavens and earth, judgment with angels recording deeds, Hell and Paradise, and culminates with exhortations to those who fear God.

Enter it in peace: this is the day of Eternity." There shall they have all that they can desire: and our's will it be to augment their bliss: And how many generations have we destroyed ere the days of these (Meccans), mightier than they in strength! Search ye then the land. Is there any escape? Lo! herein is warning for him who hath a heart, or giveth ear, and is himself an eye-witness.8 We created the heavens an…

The Koran (Al-Qur'an) primary

Muhammad (Al-Qur'an content traditionally attributed; Rodwell as translator) · c. 610–632 CE (revelations compiled into the Qur'an after the prophet’s death)
Book carefully concocted from various sources, and with much extraneous aid, and published as a divine oracle, then it would seem that the author is at once open to the charge of the grossest imposture, and even of impious blasphemy. The evidence rather shews, that in all he did and wrote, Muhammad was actuated by a sincere desire to deliver his countrymen from the grossness of its debasing idolatries–that he was urged on by an intense desire to proclaim that great truth of the Unity of the Godhead which had taken full possession of his own soul–that the end to be attained justified to his mind the means he adopted in the production of his Suras–that he worked himself up into a belief that he had received a divine call–and that he was carried on by the force of circumstances, and by gradually increasing successes, to believe himself the accredited messenger of Heaven. The earnestness of those convictions which at Mecca sustained him under persecution, and which perhaps led him, at any price as it were, and by any means, not even excluding deceit and falsehood, to endeavour to rescue his countrymen from idolatry,–naturally stiffened at Medina into tyranny and unscrupulous violence. At the same time, he was probably, more or less, throughout his whole career, the victim of a certain amount of self-deception. A cataleptic13 subject from his early youth, born–according to the traditions–of a highly nervous and excitable mother, he would be peculiarly liable to morbid and fantastic hallucinations, and alternations of excitement and depression, which would win for him, in the eyes of his ignorant countrymen, the credit of being inspired. It would be easy for him to persuade himself that he was "the seal of the Prophets," > Book is no other than a warning and a clear Koran, (6/104)

Sura 67 (The Kingdom) explains that God created death and life to test deeds, describes seven heavens and stars as a defense against satans, warns of Hell’s torment for disbelievers, and reassures believers about God’s intimate knowledge.

Moreover, if they (the Meccans) keep straight on in that way, we will surely give them to drink of abundant waters, That we may prove them thereby: but whoso withdraweth from the remembrance of his Lord, him will He send into a severe torment. It is unto God that the temples are set apart: call not then on any other therein with God. When the servant of God stood up to call upon Him, the djinn almost jostled him b…

The Koran (Al-Qur'an) primary

Muhammad (Al-Qur'an content traditionally attributed; Rodwell as translator) · c. 610–632 CE (revelations compiled into the Qur'an after the prophet’s death)
Book carefully concocted from various sources, and with much extraneous aid, and published as a divine oracle, then it would seem that the author is at once open to the charge of the grossest imposture, and even of impious blasphemy. The evidence rather shews, that in all he did and wrote, Muhammad was actuated by a sincere desire to deliver his countrymen from the grossness of its debasing idolatries–that he was urged on by an intense desire to proclaim that great truth of the Unity of the Godhead which had taken full possession of his own soul–that the end to be attained justified to his mind the means he adopted in the production of his Suras–that he worked himself up into a belief that he had received a divine call–and that he was carried on by the force of circumstances, and by gradually increasing successes, to believe himself the accredited messenger of Heaven. The earnestness of those convictions which at Mecca sustained him under persecution, and which perhaps led him, at any price as it were, and by any means, not even excluding deceit and falsehood, to endeavour to rescue his countrymen from idolatry,–naturally stiffened at Medina into tyranny and unscrupulous violence. At the same time, he was probably, more or less, throughout his whole career, the victim of a certain amount of self-deception. A cataleptic13 subject from his early youth, born–according to the traditions–of a highly nervous and excitable mother, he would be peculiarly liable to morbid and fantastic hallucinations, and alternations of excitement and depression, which would win for him, in the eyes of his ignorant countrymen, the credit of being inspired. It would be easy for him to persuade himself that he was "the seal of the Prophets," > Book is no other than a warning and a clear Koran, (91/104)

It moves from Meccan-style monotheist and revelation claims to Sura X (Jonah), “Mecca” and “109 Verses,” asserting God’s creation, signs in night and day, gardens of delight for believers, and fire for those who deny meeting Him.

to preach. When we cause man to taste our gifts of mercy, he rejoiceth in it; but if for their by-gone handy-work evil betide them, then lo! is man ungrateful. God's, the kingdom of the Heavens and of the Earth! He createth what He will! and he giveth daughters to whom He will, and sons to whom He will: Or He giveth them children of both sexes, and He maketh whom He will to be childless; for He is Wise, Powerful! …

The Koran (Al-Qur'an) primary

Muhammad (Al-Qur'an content traditionally attributed; Rodwell as translator) · c. 610–632 CE (revelations compiled into the Qur'an after the prophet’s death)
Book carefully concocted from various sources, and with much extraneous aid, and published as a divine oracle, then it would seem that the author is at once open to the charge of the grossest imposture, and even of impious blasphemy. The evidence rather shews, that in all he did and wrote, Muhammad was actuated by a sincere desire to deliver his countrymen from the grossness of its debasing idolatries–that he was urged on by an intense desire to proclaim that great truth of the Unity of the Godhead which had taken full possession of his own soul–that the end to be attained justified to his mind the means he adopted in the production of his Suras–that he worked himself up into a belief that he had received a divine call–and that he was carried on by the force of circumstances, and by gradually increasing successes, to believe himself the accredited messenger of Heaven. The earnestness of those convictions which at Mecca sustained him under persecution, and which perhaps led him, at any price as it were, and by any means, not even excluding deceit and falsehood, to endeavour to rescue his countrymen from idolatry,–naturally stiffened at Medina into tyranny and unscrupulous violence. At the same time, he was probably, more or less, throughout his whole career, the victim of a certain amount of self-deception. A cataleptic13 subject from his early youth, born–according to the traditions–of a highly nervous and excitable mother, he would be peculiarly liable to morbid and fantastic hallucinations, and alternations of excitement and depression, which would win for him, in the eyes of his ignorant countrymen, the credit of being inspired. It would be easy for him to persuade himself that he was "the seal of the Prophets," > Book is no other than a warning and a clear Koran, (97/104)

Near the end, it recounts continued guidance and revelation-advice, then begins Sura XXXIV Saba with God’s omniscience, warnings that the Hour will come, and a story of David, Solomon, and Djinn.

5 Paradise. 6 Verses 27, 28 are to be noted, as defining the proportion to be observed in rewards and punishments, the severity of the latter being only in proportion to the crime, the excellence of the former being above and beyond its strict merits. 7 But rather your own lusts. The Muhammadans believe that idols will be gifted with speech at the day of judgment. 8 The ordinary Arabic word for to die seems to be …

The Interesting Narrative of the Life of Olaudah Equiano, Or Gustavus Vassa, The African primary

Olaudah Equiano (also known as Gustavus Vassa) · 1789 (written/compiled for publication; edition-letter dated March 24, 1789)
CHAPTER I. (52/110)

Equiano describes visiting Brimstone-Hill in Montserrat, where boiling ponds of sulfurous waters turn metals black and can boil potatoes, showing the hill’s natural wonders and strange colors.

FOOTNOTES: [Footnote O: Thus was I sacrificed to the envy and resentment of this woman for knowing that the lady whom she had succeeded in my master's good graces designed to take me into her service; which, had I once got on shore, she would not have been able to prevent. She felt her pride alarmed at the superiority of her rival in being attended by a black servant: it was not less to prevent this than to be reven…

Darkwater: Voices from Within the Veil secondary

W. E. B. Du Bois (William Edward Burghardt Du Bois) · 1920 (composed/assembled for publication; modern reprints derive from the 1920 text)
CHAPTER PAGE (99/113)

Du Bois’ travel memory becomes a visionary description of the Grand Canyon, portraying it as a wound in earth and a spiritual drama that he believes exceeds ordinary material explanation.

peaks and throw their bowels to the sky. Their earth is air; their ether blood-red rock engreened. You stand upon their roots and fall into their pinnacles, a mighty mile. Behold this mauve and purple mocking of time and space! See yonder peak! No human foot has trod it. Into that blue shadow only the eye of God has looked. Listen to the accents of that gorge which mutters: "Before Abraham was, I am." Is yonder wall…

Plutarch: Lives of the noble Grecians and Romans primary

Plutarch · c. 100 CE (composed over time)
(148/1424)

Plutarch describes Artemisium’s setting, dedications to Artemis, and the tactical lessons learned after Thermopylae, while Themistocles tries to sway Ionians through inscriptions.

There the sons of Athens set The stone that freedom stands on yet. For the first step towards victory undoubtedly is to gain courage. Artemisium is in Euboea, beyond the city of Histiaea, a sea-beach open to the north; most nearly opposite to it stands Olizon, in the country which formerly was under Philoctetes; there is a small temple there, dedicated to Diana, surnamed of the Dawn, and trees about it, around which…

Plutarch: Lives of the noble Grecians and Romans primary

Plutarch · c. 100 CE (composed over time)
(603/1424)

Plutarch presents rival explanations for the victory at Aegos Potami—divine signs like Castor and Pollux, a falling stone, and astronomical theories attributed to Anaxagoras and Daimachus—before turning to Lysander’s later interpretation and aftermath.

destruction of more commanders than all the previous wars of Greece put together, it was now put an end to by the good counsel and ready conduct of one man. Some, therefore, looked upon the result as a divine intervention, and there were certain who affirmed that the stars of Castor and Pollux were seen on each side of Lysander's ship, when he first set sail from the haven toward his enemies, shining about the helm;…

Don Quixote primary

Miguel de Cervantes Saavedra · c. 1605–1615
CHAPTER I WHICH TREATS OF THE CHARACTER AND > CHAPTER XXIX. (2/5)

The pair embark and Don Quixote dismisses Sancho’s fears, making cosmological claims about crossing the equinoctial line; Sancho instead checks by touch, and they soon see water mills in the river.

“I don’t understand that logiquous,” said Sancho, “nor have I ever heard the word all the days of my life.” “Longinquous,” replied Don Quixote, “means far off; but it is no wonder thou dost not understand it, for thou art not bound to know Latin, like some who pretend to know it and don’t.” “Now they are tied,” said Sancho; “what are we to do next?” “What?” said Don Quixote, “cross ourselves and weigh anchor; I me…

The Anglo-Saxon Chronicle primary

(Anglo-Saxon Chronicle; translator/editor) James Ingram · c. 890–mid-12th century (chronicle compilation and ongoing additions); modern translation ed. 1823/1847
(13/157)

The Anglo-Saxon Chronicle begins by describing early peoples and Roman involvement: Julius Caesar fights Britons, loses part of his army, and later dates Christian events, including Herod’s persecution and Christ’s birth, baptism, and crucifixion.

occupationibus meis ignoscas; premor enim oneribus, et typographiae cura, ut vix sustineam." Who could be angry after this? (37) Miss Gurney, of Keswick, Norfolk. The work, however, was not published. THE ANGLO-SAXON CHRONICLE The island Britain (1) is 800 miles long, and 200 miles broad. And there are in the island five nations; English, Welsh (or British) (2), Scottish, Pictish, and Latin. The first inhabitants …

The Voyage of the Beagle primary

Charles Darwin · 1831-1836 (journal of the voyage; later edited/condensed for publication)
CHAPTER I (11/13)

Darwin records sailing from Bahia, observing Red Sea–type Trichodesmium erythraeum “sea-sawdust” confervae that discolor the ocean in long bands near Abrolhos and elsewhere, including near Keeling Atoll in the Indian Ocean.

but through the sides of the monster, which has thus been killed. Who would ever have imagined that a little soft fish could have destroyed the great and savage shark? March 18th.--We sailed from Bahia. A few days afterwards, when not far distant from the Abrolhos Islets, my attention was called to a reddish-brown appearance in the sea. The whole surface of the water, as it appeared under a weak lens, seemed as if…

The Voyage of the Beagle primary

Charles Darwin · 1831-1836 (journal of the voyage; later edited/condensed for publication)
CHAPTER I > CHAPTER VIII (17/28)

He vividly describes phosphorescent seas with glowing waves, explains it via gelatinous particles and ocean purification by decomposition, and notes similar luminance patterns at depths and near Fernando Noronha.

every wave was bright, and the sky above the horizon, from the reflected glare of these livid flames, was not so utterly obscure as over the vault of the heavens. As we proceed further southward the sea is seldom phosphorescent; and off Cape Horn I do not recollect more than once having seen it so, and then it was far from being brilliant. This circumstance probably has a close connection with the scarcity of organ…

The Voyage of the Beagle primary

Charles Darwin · 1831-1836 (journal of the voyage; later edited/condensed for publication)
CHAPTER I > CHAPTER XI (7/17)

Darwin contrasts land and sea life in Patagonia, arguing that the insect fauna is not shared with other regions, while rocky shores teem with marine animals, notably the kelp Macrocystis pyrifera.

Patagonia; and the difference is strongly exemplified in the entomology. I do not believe they have one species in common; certainly the general character of the insects is widely different. If we turn from the land to the sea, we shall find the latter as abundantly stocked with living creatures as the former is poorly so. In all parts of the world a rocky and partially protected shore perhaps supports, in a given s…

The Voyage of the Beagle primary

Charles Darwin · 1831-1836 (journal of the voyage; later edited/condensed for publication)
CHAPTER I > CHAPTER XIV (1/17)

Darwin recounts his sailing from Low's Harbour to San Carlos, Chiloe, while Osorno erupts and he notes simultaneous eruptions and earthquakes at Aconcagua and Coseguina.

CHILOE AND CONCEPCION: GREAT EARTHQUAKE San Carlos, Chiloe--Osorno in eruption, contemporaneously with Aconcagua and Coseguina--Ride to Cucao--Impenetrable Forests--Valdivia Indians--Earthquake--Concepcion--Great Earthquake--Rocks fissured--Appearance of the former Towns--The Sea Black and Boiling--Direction of the Vibrations--Stones twisted round--Great Wave--Permanent Elevation of the Land--Area of Volcanic Phenom…

The Voyage of the Beagle primary

Charles Darwin · 1831-1836 (journal of the voyage; later edited/condensed for publication)
CHAPTER I > CHAPTER XIV (16/17)

He argues the earthquake’s most remarkable effect was permanent land uplift around the Bay of Concepción, cites raised tidal-shell evidence at S. Maria and Valparaiso, and suggests successive small uprisings.

it would also appear that the wave is larger or smaller, according to the extent of shoal water which has been agitated together with the bottom on which it rested. The most remarkable effect of this earthquake was the permanent elevation of the land, it would probably be far more correct to speak of it as the cause. There can be no doubt that the land round the Bay of Concepcion was upraised two or three feet; but…

The Voyage of the Beagle primary

Charles Darwin · 1831-1836 (journal of the voyage; later edited/condensed for publication)
CHAPTER I > CHAPTER XVI (6/28)

Darwin argues that Coquimbo’s raised shell terraces imply recent sea submergence and ongoing coastal uplift, noting the rarity of recent shell strata elsewhere on the Pacific coast and linking preservation to slow continental rising.

along the whole coast-line of Patagonia. They have undoubtedly been formed by the denuding power of the sea, during long periods of rest in the gradual elevation of the continent. Shells of many existing species not only lie on the surface of the terraces at Coquimbo (to a height of 250 feet), but are embedded in a friable calcareous rock, which in some places is as much as between twenty and thirty feet in thicknes…

Relativity: The Special and General Theory primary

Albert Einstein · 1916
Part I: The Special Theory of Relativity > PART II: THE GENERAL THEORY OF RELATIVITY (3/19)

Einstein reframes gravity as a field analogous to electromagnetic fields, stating that free fall acceleration depends only on the gravitational field and not on the body’s material or physical state.

be theoretically represented much more satisfactorily than without it, and this applies particularly to the transmission of electromagnetic waves. The effects of gravitation also are regarded in an analogous manner. The action of the earth on the stone takes place indirectly. The earth produces in its surrounding a gravitational field, which acts on the stone and produces its motion of fall. As we know from experien…

Relativity: The Special and General Theory primary

Albert Einstein · 1916
Part I: The Special Theory of Relativity > PART II: THE GENERAL THEORY OF RELATIVITY (14/19)

Einstein states that in special relativity the space-time interval ds^2 is preserved across all Galilean reference bodies under Lorentz transformations, and he extends this invariant “distance” to a four-dimensional continuum that can be treated like Euclidean space using an imaginary time coordinate.

*ds*2 = *dx*12 + *dx*22 + *dx*32 + *dx*42. In this case relations hold in the four-dimensional continuum which are analogous to those holding in our three-dimensional measurements. However, the Gauss treatment for *ds*2 which we have given above is not always possible. It is only possible when sufficiently small regions of the continuum under consideration may be regarded as Euclidean continua. For example, this ob…

Relativity: The Special and General Theory primary

Albert Einstein · 1916
Part I: The Special Theory of Relativity (9/11)

Einstein argues that clocks in gravitational or rotating systems run at different rates depending on potential, treating atoms emitting light as clocks and predicting spectral lines shift toward the red near massive bodies.

image053 It may be added that, according to the theory, half of this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification (“curvature”) of space caused by the sun. This result admits of an experimental test by means of the photographic registration of stars during a total eclipse of the sun. The only reason why we must wait for a total eclipse is…

Relativity: The Special and General Theory primary

Albert Einstein · 1916
Part I: The Special Theory of Relativity (10/11)

Einstein describes cosmological developments after his first edition: Friedman’s expanding-space solutions without a cosmological term, and Hubble’s observed redshift in extra-galactic nebulae, while noting unresolved timing and finiteness questions.

image057 If we represent the difference of potential of the centrifugal force between the position of the clock and the centre of the disc by φ, *i.e.* the work, considered negatively, which must be performed on the unit of mass against the centrifugal force in order to transport it from the position of the clock on the rotating disc to the centre of the disc, then we have image058 From this it follows that image…

Relativity: The Special and General Theory primary

Albert Einstein · 1916
Part I: The Special Theory of Relativity (11/11)

In the Appendix on the structure of space, Einstein describes earlier static cosmology with an assumed constant matter density and radius, then notes Friedman’s expansion solution without a cosmological term, and links Hubble’s redshift observations to an expanding universe while highlighting a timing inconsistency.

of spectral lines be definitely traced to the gravitational potential, then the study of this displacement will furnish us with important information as to the mass of the heavenly bodies.[27] [27] The displacement of spectral lines towards the red end of the spectrum was definitely established by Adams in 1924, by observations on the dense companion of Sirius, for which the effect is about thirty times greater t…

History of Florence and of the Affairs of Italy secondary

Niccolò Machiavelli · 1521-1525 (composed)
BOOK I > CHAPTER VII (2/5)

In 1456 a violent Adriatic whirlwind and hurricane-like storm devastate parts of Tuscany near St. Casciano and the hills between Pisa and Grieve, which the author interprets as divine warning rather than punishment.

war; and in Hungary their zeal was cooled through the death of Giovanni Corvini the Waiwode, who commanded the Hungarian forces on that memorable occasion, and fell in the battle. To return to the affairs of Italy. In the year 1456, the disturbances occasioned by Jacopo Piccinino having subsided, and human weapons laid aside, the heavens seemed to make war against the earth; dreadful tempestuous winds then occurring…

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER III (1/3)

He explains vocal pitch across nations using a celestial geometry model—horizon, axis, and the pole star—and compares the resulting heavenly shape to the Greek sambuca instrument.

PROPORTIONS OF THE PRINCIPAL ROOMS 1. There are five different styles of cavaedium, termed according to their construction as follows: Tuscan, Corinthian, tetrastyle, displuviate, and testudinate. In the Tuscan, the girders that cross the breadth of the atrium have crossbeams on them, and valleys sloping in and running from the angles of the walls to the angles formed by the beams, and the rainwater falls down alon…

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER I (2/4)

He describes a geocentric cosmos with the heaven rotating around axes, the belt of twelve zodiac signs, and the opposing west-to-east motion of the moon and planets through the signs.

moon makes her circuit of the heaven in twenty-eight days plus about an hour, and with her return to the sign from which she set forth, completes a lunar month. 6. The sun takes a full month to move across the space of one sign, that is, one twelfth of the firmament. Consequently, in twelve months he traverses the spaces of the twelve signs, and, on returning to the sign from which he began, completes the period of …

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER I (3/4)

Vitruvius gives quantitative orbital periods for the moon, Mercury, Venus, Mars, Jupiter, and Saturn, explaining retrograde pauses as effects of the sun’s heat and rays forming an equilateral-triangle divergence.

before. He is, as it appears, slower, because the nearer he is to the outermost part of the firmament, the greater is the orbit through which he has to pass. 11. The three that complete their circuits above the sun's course do not make progress while they are in the triangle which he has entered, but retrograde and pause until the sun has crossed from that triangle into another sign. Some hold that this takes place …

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER I (4/4)

He supports the sun-heat explanation with an ant-on-a-wheel analogy and proposes that planets’ relative heat or cold depends on their position near the outer frozen regions of the firmament.

to the earth, the sooner they are seen to finish their courses; for those of them that have a smaller orbit often pass those that are higher, going under them. 15. For example, place seven ants on a wheel such as potters use, having made seven channels on the wheel about the centre, increasing successively in circumference; and suppose those ants obliged to make a circuit in these channels while the wheel is turned …

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER II

According to Berosus and then Aristarchus of Samos, Vitruvius explains lunar phases via the moon’s partial illumination—either turning toward the sun’s light or reflecting it as a mirror.

THE PHASES OF THE MOON 1. According to the teaching of Berosus, who came from the state, or rather nation, of the Chaldees, and was the pioneer of Chaldean learning in Asia, the moon is a ball, one half luminous and the rest of a blue colour. When, in the course of her orbit, she has passed below the disc of the sun, she is attracted by his rays and great heat, and turns thither her luminous side, on account of the …

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER IV

Vitruvius describes positions of the Great Bear, Virgin, Arcturus, Charioteer, Perseus, Andromeda, Cassiopea, and other northern constellations and names specific bright stars within them.

THE NORTHERN CONSTELLATIONS 1. The Great Bear, called in Greek [Greek: arktos] or [Greek: helikê], has her Warden behind her. Near him is the Virgin, on whose right shoulder rests a very bright star which we call Harbinger of the Vintage, and the Greeks [Greek: protrygêtês]. But Spica in that constellation is brighter. Opposite there is another star, coloured, between the knees of the Bear Warden, dedicated there un…

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER V

He outlines southern constellations and explains why some stars never rise, citing stars like Canopus that are known only through reports from distant travellers in Egypt.

THE SOUTHERN CONSTELLATIONS 1. First, under the He-Goat lies the Southern Fish, facing towards the tail of the Whale. The Censer is under the Scorpion's sting. The fore parts of the Centaur are next to the Balance and the Scorpion, and he holds in his hands the figure which astronomers call the Beast. Beneath the Virgin, Lion, and Crab is the twisted girdle formed by the Snake, extending over a whole line of stars, …

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER VI

Vitruvius connects the revolution of the firmament and the signs’ influence with astronomy, defers astrology and nativities to Chaldeans, and lists Greek and Roman astronomers’ weather work.

ASTROLOGY AND WEATHER PROGNOSTICS 1. I have shown how the firmament, and the twelve signs with the constellations arranged to the north and south of them, fly round the earth, so that the matter may be clearly understood. For it is from this revolution of the firmament, from the course of the sun through the signs in the opposite direction, and from the shadows cast by equinoctial gnomons, that we find the figure of…

The Ten Books on Architecture primary

Vitruvius Pollio · c. 30–20 BCE
BOOK I > CHAPTER VIII (3/3)

Vitruvius explains how the water flow through a rim opening varies with the sun’s position in zodiac signs, thereby lengthening or shortening days and hours for equinoxes, solstices, and months.

it at the bottom, Libra at the spectator's right, Aries at his left, and let the other signs be given places between them as they are seen in the heavens. 13. Hence, when the sun is in Capricornus, the tongue on the rim touches every day one of the points in Capricornus on the lip of the larger drum, and is perpendicular to the strong pressure of the running water. So the water is quickly driven through the opening …

History of the Expedition under the Command of Captains Lewis and Clark, Vol. 1. primary

Meriwether Lewis · 1804-1806 (narrative materials compiled from journals; edited for press by Paul Allen for 1814 publication)
CHAPTER I. > CHAPTER VI. (4/16)

January 14th–February 8th covers astronomy for longitude, continued diplomatic engagement with Minnetarees and Mandans, the use of rattle-serpent medicine during childbirth, horse management against theft, and prolonged hunting trips when game and buffalo disappear.

that of yesterday the weather to-day was cold and clear, the thermometer standing at 38 degrees below 0. Poscopsahe and Shotahawrora visited us, and past the night at the fort. Saturday 12. The weather continues very cold, the mercury at sunrise being 20 degrees below 0. Three of the hunters returned, having killed three elk. Sunday 13. We have a continuation of clear weather, and the cold has increased, the mercur…

History of the Expedition under the Command of Captains Lewis and Clark, Vol. 1. primary

Meriwether Lewis · 1804-1806 (narrative materials compiled from journals; edited for press by Paul Allen for 1814 publication)
CHAPTER I. > CHAPTER VII. (8/18)

On Friday 12 they spend the day making celestial observations at the mouth of the Little Missouri, giving detailed measurements of the river and its geology, plants, and sparse game.

black. Under a bluff opposite to our encampment we discovered some Indians with horses, whom we supposed were Minnetarees, but the width of the river prevented our speaking to them. Friday, 12th. We set off early and passed a high range of hills on the south side, our periogues being obliged to go over to the south in order to avoid a sandbank which was rapidly falling in. At six miles we came to at the lower side o…

History of the Expedition under the Command of Captains Lewis and Clark, Vol. 1. primary

Meriwether Lewis · 1804-1806 (narrative materials compiled from journals; edited for press by Paul Allen for 1814 publication)
CHAPTER I. > CHAPTER IX. (17/18)

On Thursday 6, Lewis decides the explored river runs too far north for the Pacific, fails to secure a meridian altitude due to cloud, prepares rafts but abandons them as wet-baggage risks, and returns on foot toward Lark creek despite cold storms and rain.

strong steady current. The party had killed five elk, and a mule-deer; and by way of experiment roasted the burrowing squirrels, which they found to be well flavoured and tender. Thursday 6. Captain Lewis was now convinced that this river pursued a direction too far north for our route to the Pacific, and therefore resolved to return; but waited till noon to take a meridian altitude. The clouds, however, which had g…

History of the Expedition under the Command of Captains Lewis and Clark, Vol. 1. primary

Meriwether Lewis · 1804-1806 (narrative materials compiled from journals; edited for press by Paul Allen for 1814 publication)
CHAPTER I. > CHAPTER X. (4/17)

On Monday 10 they dry baggage, build caches (hiding provisions and goods for years) near the Missouri, secure a periogue at Maria’s river entrance, and record meridian latitude; they also note birds like kingbird and beemartin.

dry channels which we passed on the south, and the travels of Mr. Fidler forbid us to believe that it could have been obtained from the mountains towards the northwest. These observations which satisfied our mind completely we communicated to the party: but every one of them were of a contrary opinion; and much of their belief depended on Crusatte, an experienced waterman on the Missouri, who gave it as his decided …

An Essay Concerning Humane Understanding, Volume 1 secondary

John Locke · 1689
BOOK I NEITHER PRINCIPLES NOR IDEAS ARE INNATE > CHAPTER IV. (3/4)

Locke differentiates solidity from hardness and contends that even soft bodies resist as much if they remain between others; he uses examples like air in a football and a water-filled gold globe experiment said to be made at Florence.

change figure by the pressure of any part of our bodies; and that, on the contrary, soft, which changes the situation of its parts upon an easy and unpainful touch. But this difficulty of changing the situation of the sensible parts amongst themselves, or of the figure of the whole, gives no more solidity to the hardest body in the world than to the softest; nor is an adamant one jot more solid than water. For, thou…

An Essay Concerning Humane Understanding, Volume 1 secondary

John Locke · 1689
BOOK I NEITHER PRINCIPLES NOR IDEAS ARE INNATE > CHAPTER XXX. (2/2)

Locke distinguishes real from fantastical ideas by whether they match natural reality and archetypes, then argues simple ideas are always real appearances produced by powers in things.

4. Mixed Modes and Relations, made of consistent Ideas, are real. Secondly, MIXED MODES and RELATIONS, having no other reality but what they have in the minds of men, there is nothing more required to this kind of ideas to make them real, but that they be so framed, that there be a possibility of existing conformable to them. These ideas themselves, being archetypes, cannot differ from their archetypes, and so canno…

Voyages in Search of the North-West Passage secondary

Richard Hakluyt · c. 1580s–c. 1600 (compiled translations/collections of voyages; multiple editions and supplements)
(4/13)

Parry’s 1827 over-ice attempt toward the North Pole is summarized: progress is tiny because the ice drifts, red snow and polar fauna are noted, and the party reaches about 82°45′.

This is "the pack," the edge of a great ice-field broken by the swell. It is a perilous and an exciting thing to push through pack ice in a gale. Now there is ice as far as eye can see, that is "an ice-field." Masses are forced up like colossal tombstones on all sides; our sailors call them "hummocks;" here and there the broken ice displays large "holes of water." Shall we go on? Upon this field, in 1827, Parry a…

The Travels of Marco Polo — Volume 1 primary

Marco Polo · c. 1298 (Book of Marco Polo)
C.S.I., Major-General KEYES, C.B., Dr. GEORGE BIRDWOOD, Mr. BURGESS, of > CHAPTER XVIII. (10/11)

The editor explains Marco Polo’s “magical darkness” via dry fogs and dust storms, citing examples from Sind and Kerman, discusses Tartar beliefs about enchantment, and notes a textual peculiarity about how many survived.

no personal knowledge of Upper India, I now think it probable that Marsden was right, and that *Dilivar* is really a misunderstanding of “*Città* di Livar” for *Lahàwar* or Lahore. The *Magical darkness* which Marco ascribes to the evil arts of the Karaunas is explained by Khanikoff from the phenomenon of _Dry Fog_, which he has often experienced in Khorasan, combined with the *Dust Storm* with which we are fa…

The Travels of Marco Polo — Volume 1 primary

Marco Polo · c. 1298 (Book of Marco Polo)
C.S.I., Major-General KEYES, C.B., Dr. GEORGE BIRDWOOD, Mr. BURGESS, of > CHAPTER XXXIII. (1/12)

In Cambaluc the Great Kaan supports thousands of astrologers from different faiths, who use an astrolabe to predict weather and events, sell annual almanacs called Tacuin, and cast horoscopes based on birth time using a 12-year animal cycle.

[CONCERNING THE ASTROLOGERS IN THE CITY OF CAMBALUC.] [There are in the city of Cambaluc, what with Christians, Saracens, and Cathayans, some five thousand astrologers and soothsayers, whom the Great Kaan provides with annual maintenance and clothing, just as he provides the poor of whom we have spoken, and they are in the constant exercise of their art in this city. They have a kind of astrolabe on which are inscr…

The Travels of Marco Polo — Volume 1 primary

Marco Polo · c. 1298 (Book of Marco Polo)
C.S.I., Major-General KEYES, C.B., Dr. GEORGE BIRDWOOD, Mr. BURGESS, of > CHAPTER XXXIII. (2/12)

The text discusses the Latin and Italian use of the term Taccuino/Taquím almanac, notes Chinese government printing of calendars, and describes how imperial almanacs mark lucky and unlucky days for daily decisions under penalty for counterfeiting.

for making a journey, and so forth. They put entire faith in it, and whoever can afford one governs himself in all things by its rules.” (Bk. V. ch. xiv.) The use of the term by Marco may possibly be an illustration of what I have elsewhere propounded, viz. that he was not acquainted with Chinese, but that his intercourse and conversation lay chiefly with the foreigners at the Kaan’s Court, and probably was ca…

The Travels of Marco Polo — Volume 1 primary

Marco Polo · c. 1298 (Book of Marco Polo)
C.S.I., Major-General KEYES, C.B., Dr. GEORGE BIRDWOOD, Mr. BURGESS, of > CHAPTER XXXIII. (3/12)

A long explanatory note lists two types of Chinese calendars (Wan-nien-shu and the Annual Calendar), including cyclical signs, intercalary months, zodiac positions, and auspicious days, and claims such superstitions entered under earlier dynasties.

the *édition de luxe*; but as these prices were in paper-money it is extremely difficult to say, in the varying depreciation of that currency, what the price really amounted to. [“The Calendars for the use of the people, published by Imperial command, are of two kinds. The first, _Wan-nien-shu, the Calendar of Ten Thousand Years_, is an abridgment of the Calendar, comprising 397 years, viz. from 1624 to 2020. …

The Travels of Marco Polo — Volume 2 primary

Marco Polo (translated by Sir Henry Yule, revised by Henri Cordier) · c. 1298-1299
BOOK SECOND—(*Continued*). > CHAPTER XIV. (4/4)

Further notes compile accounts of Ceylon’s rubies, Adam’s Peak traditions, and Chinese terminology for Ceylon stones, including a claim that gems are congealed tears of Buddha.

for Andrea Corsali (1515) says: “They tell that the king of this island possesses two rubies of colour so brilliant and vivid that they look like a flame of fire.” Sir E. Tennent, on this subject, quotes from a Chinese work a statement that early in the 14th century the Emperor sent an officer to Ceylon to purchase a carbuncle of unusual lustre. This was fitted as a ball to the Emperor’s cap; it was upwards of…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER I. (1/9)

Strabo argues that geography belongs to philosophy and can be grounded in the knowledge of Homer and earlier thinkers, using Homer’s descriptions of the ocean, distant lands, and celestial phenomena.

1.[1] If the scientific investigation of any subject be the proper avocation of the philosopher, Geography, the science of which we propose to treat, is certainly entitled to a high place; and this is evident from many considerations. They who first ventured to handle the matter were distinguished men, Homer, Anaximander the Milesian, and Hecatæus, (his fellow-citizen according to Eratosthenes,) Democritus, Eudoxus, …

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER I. (2/9)

Strabo interprets Homer’s references to Oceanus, the Arctic Circle via the Bear/Wain, and northern peoples, arguing that Homer understood the northern boundary where stars and sea horizons meet.

“Only star of those denied To slake his beams in Ocean’s briny baths.”[14] Now, by the “Bear” and the “Wain,” he means the Arctic Circle; otherwise he would never have said, “It *alone* is deprived of the baths of the ocean,” when such an *infinity* of stars is to be seen continually revolving in that part of the hemisphere. Let no one any longer blame his ignorance for being merely acquainted with one Bear, when th…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER I. (3/9)

Strabo continues to defend Homer’s oceanic cosmology, debating whether Homer’s ocean imagery refers to tides and flow, and concludes that the ocean behaves as one connected system around the earth.

“Each day she thrice disgorges, and again Thrice drinks, insatiate, the deluge down.”[20] The assertion of thrice, instead of twice, is either an error of the author, or a blunder of the scribe, but the phenomenon is the same, and the expression soft-flowing,[21] has reference to the flood-tide, which has a gentle swell, and does not flow with a full rush. Posidonius believes that where Homer describes the rocks as …

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER I. (4/9)

He claims that the inhabited world is an island because distant coasts are surrounded by water, that circumnavigation is plausible, and that the uniformity of ocean tides supports a single ocean.

the increase and diminution, is every where identical, or at all events has but little difference, as if produced by the agitation of one sea, and resulting from one cause. 9. We must not credit Hipparchus, who combats this opinion, denying that the ocean is every where similarly affected; or that even if it were, it would not follow that the Atlantic flowed in a circle, and thus continually returned into itself. Se…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER II. (12/27)

Strabo defends Homer’s geographical knowledge of winds and climates by quoting passages about Ithaca’s westward position and seasonal directions, and criticizes Eratosthenes for reading Homer’s wind statements too absolutely.

respect to the winds and climates, Homer shows the wide extent of his geographical knowledge, for in his topographical descriptions he not unfrequently informs us of both these matters. Thus, “My abode Is sun-burnt Ithaca. Flat on the deep she lies, farthest removed Toward the west, while situate apart, Her sister islands face the rising day.”[150] And, “It has a two-fold entrance, One towards the n…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER II. (13/27)

Strabo discusses competing ancient theories of wind types, arguing that Homer’s “stormy” and “clear” zephyrs correspond to specific modern-direction winds, and he corrects Eratosthenes’ account of Homer’s meteorology.

“As when two adverse winds, blowing from Thrace, Boreas and Zephyrus.”[170] But Posidonius remarks that none of those who are really acquainted with these subjects, such as Aristotle, Timosthenes, and Bion the astronomer, entertain so mistaken an opinion in regard to the winds. They say that the north-east (Cæcias) blows from the commencement of summer, and that the south-west wind (Libs), which is exactly opposite …

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER III. (1/7)

Strabo argues that five zones best explain celestial appearances, atmospheric temperature, and geography, and criticizes Polybius and Posidonius for using inconsistent boundaries or basing zones on nations rather than physical causes.

1. Polybius supposes six zones: two situated between the poles and the arctic circles; two between the arctic circles and the tropics; and two between the tropics which are divided by the equator. However, it appears to me that the division into five zones accords best both with the order of external nature and geography. With external nature, as respects the celestial phenomena, and the temperature of the atmosphere…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER IV. (5/5)

Strabo critiques Polybius’ method of measuring inhabited earth by celestial risings rather than fixed distances, then reviews promontories and regional divisions of Europe and sets out to correct further errors.

us that its direction was contrary to that of the Nile, and, so to speak, diametrically opposite thereto, as if the course of both rivers lay under the same meridian. 7. Further, the length of the inhabited earth is measured on a line parallel with the equator, as it is in this direction that its greatest length lies: in the same way with respect to each of the continents, we must take their length as it lies betwee…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER V. (2/23)

He defines “perfect sciences,” then lays out natural-philosophy astronomy foundations: Earth and heavens are spheroidal; weighted bodies tend to a center; Earth is motionless while heavens and fixed stars turn; zones and circular celestial motions guide geography.

as those which, depending on no external hypothesis, have their origin, and the evidence of their propositions, in themselves. Here are a few of the facts established by natural philosophers.[705] The earth and heavens are spheroidal. The tendency of all bodies having weight, is to a centre. Further, the earth being spheroidal, and having the same centre as the heavens, is motionless, as well as the axis which pas…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER V. (3/23)

Strabo explains dividing heaven and Earth into five zones using parallels to the equator, distinguishes inhabited temperate zones by hemisphere, and asserts that “we” are in the northern hemisphere; he also discusses the mismatch of climates and the absence of the supposed torrid region.

torrid region. Nor is there any portion of it to be found in which the *climata* are opposite to those which have been described as characterizing the northern temperate zone. 4. Assuming these data, and availing himself likewise of astronomical observations, by which the position of every place is properly determined, whether with respect to the circles parallel to the equator, or to those which cut these latter at…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER V. (4/23)

Using astronomically determined positions, Strabo describes how to measure Earth’s globe—equator to pole distance and multiplying by four—then sets out the geographer’s role: adopting prior size/form facts and correcting earlier authorities.

cutting the two preceding circles at right angles. The northern hemisphere contains two quarters of the earth, which are bounded by the equator and the circle passing through the poles. Each of these [quarters] should be supposed to contain a four-sided district, its northern side being composed of one half of the parallel next the pole; its southern, by the half of the equator; and its remaining sides, by [two] seg…

The Geography of Strabo, Volume 1 (of 3) primary

Strabo · c. 20 CE (Books I–VI likely composed/available by this period)
BOOK I. > CHAPTER V. (7/23)

Drawing on Hipparchus and Eratosthenes, he uses solstice observations at Syene, distances along the Nile toward Meroe and Alexandria, and voyage-based routes (Alexandria to Rhodes to Byzantium and the Dnieper) to set southern and northern climate boundaries of habitable Earth.

by tribute, after deducting the wages of the soldiers necessary for guarding the island and exacting the taxes. And the other islands adjacent to this would be still more unproductive. 9. If, then, to the distance between Rhodes and the Dnieper be added four thousand stadia north of the latter place, the whole would come to 12,700 stadia; and since from Rhodes to the southern limit of the habitable earth there are 1…