The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...

USE.

* 1.1 ERatosthenes applyeth those Proposi∣tions to the measuring of the Circum∣ference of the Earth. He supposeth that two Rays of Light proceeding from the Center of the Sun to Two Points on the Earth, are Physically Parallel: He sup∣poseth also that at Syena a Town in Egypt, the Sun was in the zenith on the day of the Solstice, because that their Cisterns, Wells, and such like, were enlightned by the Suns Rays to the very bottom, he measu∣red also the distance from Alexandria to Syena. To Demonstrate which, let us suppose Alexandrea to be Situated at the Point B, and Syena at the Point A, where let the Style BC be erected Perpendi∣cular to the Horizon, and let DF, EC, be Two Rays proceeding from the Center of the Sun, when in the Solstice, which are Parallels between themselves; let DA that Ray of Light Perpendicular to Syena, be supposed to be continued to F, the Center of the Earth.

Now having observed at Alexandria the Angle GCB, which is made or in∣cluded between the Perpendicular CB, and the Ray of Light EC: I say that

because the aforesaid Rays are Parallel, the Alternate Angles GCB, BFA, are equal. We know then the Angle AFB, and the measure of AB the distance of Alexandria to Syena taken in Degrees. Now supposing this Distance be known in Miles, the Circumference of the Earth shall be easily found by a simple Rule of Three: For if so many Degrees give so many Miles, what shall 360.

Notes

• * 1.1

  Use 29.