To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
THat it is a hard matter exactly to determine the true Magnitude of the coelestial bodies, is not I beleeve denied by any, it will be therefore sufficient if we shall determine them so, as that there be no sensible errour in them; and to such exactnesse, we may traine by the rules and proportions following.
As the Semidiameter of the Earths shadow C B I. Is to the Semidia∣meter of the shadow in parts of the Earths Semidiameter C I = B K: So is the apparent Semidiameter of the Moon. To the Semidiameter of the Moone in parts of the Ear••hs Semidiameter, that is
| As C B I | 77471 co. ar. | 10. 1108609 |
| To C I | 7640 | 1. 8831496 |
| So is the Moones semid. | 28333 | 1. 4522925 |
| To the Moones semid. | 27945 | 1. 4463030 |
And Sphears being in triplicated proportion of their diameters, the pro∣portion of the earth to the Moone will be as 1. 00000. 00000. 00000. the Cube of the earths Semidiameter to 02182. 28939. 33625. the Cube of the Moones semid. 27945. and therefore dividing the earths Semidiame∣ter by the Moons, the quotient will be 45. 823, and so many times is the body of the Moon contained in the Earth.
The proportion between the Semidiameter of the Earth and the Semidi∣ameter of the Sun, may be found by this analogy,
| As Radius | 90 | |
| To A B | 1440. 66 | 3. 1585614 |
| So is tang. A B E | 27916 | 7. 687706•• |
| To A E | 7. 0189 | 0. 8462683 |
| But if to A B | 1440. 66 | |
| You adde B D | 239. 43 | |
| Their summe is A D | 1680. 09 | |
| And then, As Radius | 90 | |
| To the side A D | 1680. 09 | 3. 2255415 |
| So is tang. of A D E or K I G | 23928 | 7. 6207755 |
| To A E | 7. 0197 | 0. 8463170 |
And now if you take the lesser semidiameter of the Sun, the Cube there∣of will be ••45. 781, but taking the Semidiameter of the Sun to be but 7 semidiameters of the earth, the Sun will be 343 times bigger then the Earth.
The proportion of the Semidiameter of the earth and the Moone is as 1 to 27945, of the Sun and the Earth as 7 to 1, and therefore of the Sun and the Moon as 7 to 27945. The Cube of 7 is 343, the Cube of 27945 is 02182, &c, by which dividing the Cube of the Suns semidiameter the quotient will be 15717. 47 and so many times is the Moone contained in the Sun.