Second Argument.
Some say that the stars appear most brilliant at night in proportion as they are higher up; and that if they had no light of their own, the shadow of the earth which comes between them and the sun, would darken them, since they would not face nor be faced by the solar body. But those persons have not considered that the conical shadow of the earth cannot reach many of the stars; and even as to those it does reach, the cone is so much diminished that it covers very little of the star's mass, and all the rest is illuminated by the sun.
913.
Why the planets appear larger in the East than they do overhead, whereas the contrary should be the case, as they are 3500 miles nearer to us when in mid sky than when on the horizon.
All the degrees of the elements, through which the images of the celestial bodies pass to reach the eye, are equal curves and the angles by which the central line of those images passes through them, are unequal angles [Footnote 13: inequali, here and elsewhere does not mean unequal in the sense of not being equal to each other, but angles which are not right angles.]; and the distance is greater, as is shown by the excess of a b beyond a d; and the enlargement of these celestial bodies on the horizon is shown by the 9th of the 7th.
Observations on the stars.
914.
To see the real nature of the planets open the covering and note at the base [Footnote 4: basa. This probably alludes to some instrument, perhaps the Camera obscura.] one single planet, and the reflected movement of this base will show the nature of the said planet; but arrange that the base may face only one at the time.
On history of astronomy.
915.
Cicero says in [his book] De Divinatione that Astrology has been practised five hundred seventy thousand years before the Trojan war.
57000.
[Footnote: The statement that CICERO, De Divin. ascribes the discovery of astrology to a period 57000 years before the Trojan war I believe to be quite erroneous. According to ERNESTI, Clavis Ciceroniana, CH. G. SCHULZ (Lexic. Cicer.) and the edition of De Divin. by GIESE the word Astrologia occurs only twice in CICERO: De Divin. II, 42. Ad Chaldaeorum monstra veniamus, de quibus Eudoxus, Platonis auditor, in astrologia judicio doctissimorum hominum facile princeps, sic opinatur (id quod scriptum reliquit): Chaldaeis in praedictione et in notatione cujusque vitae ex natali die minime esse credendum." He then quotes the condemnatory verdict of other philosophers as to the teaching of the Chaldaeans but says nothing as to the antiquity and origin of astronomy. CICERO further notes De oratore I, 16 that Aratus was "ignarus astrologiae" but that is all. So far as I know the word occurs nowhere else in CICERO; and the word Astronomia he does not seem to have used at all. (H. MULLER-STRUBING.)]
Of time and its divisions (916-918).
916.
Although time is included in the class of Continuous Quantities, being indivisible and immaterial, it does not come entirely under the head of Geometry, which represents its divisions by means of figures and bodies of infinite variety, such as are seen to be continuous in their visible and material properties. But only with its first principles does it agree, that is with the Point and the Line; the point may be compared to an instant of time, and the line may be likened to the length of a certain quantity of time, and just as a line begins and terminates in a point, so such a space of time. begins and terminates in an instant. And whereas a line is infinitely divisible, the divisibility of a space of time is of the same nature; and as the divisions of the line may bear a certain proportion to each other, so may the divisions of time.
[Footnote: This passage is repeated word for word on page 190b of the same manuscript and this is accounted for by the text in Vol. I, No. 4. Compare also No. 1216.]
917.
Describe the nature of Time as distinguished from the Geometrical definitions.
918.
Divide an hour into 3000 parts, and this you can do with a clock by making the pendulum lighter or heavier.