Short, but yet plain elements of geometry. Shewing how by a brief and easie method, most of what is necessary and useful in Euclid, Archimedes, Apollonius, and other excellent geometricians, both ancient and modern, may be understood / Written in French by F. Ignat. Gaston Pardies. And render'd into English, by John Harris.
- Ignace-Gaston Pardies
- Date:
- 1725
Licence: Public Domain Mark
Credit: Short, but yet plain elements of geometry. Shewing how by a brief and easie method, most of what is necessary and useful in Euclid, Archimedes, Apollonius, and other excellent geometricians, both ancient and modern, may be understood / Written in French by F. Ignat. Gaston Pardies. And render'd into English, by John Harris. Source: Wellcome Collection.
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![34. All Rectangles, having the fame or equal Heights, are to one another as their Bafes, and ha. ving the fame Bafes their Heights are equal. Let the Rectangles A and B be between the fame parallel Lines dfandca; fo that adbe equalto cf: then do I fay, that A:B::ab: be. ¢_e___q Thar the Rectangle A is to the Rect. ÿ [B] A | angle B, as the Bafe a b to the Bale be: cb 4 And that if, for Inftance, ab be double to bc, then fhall A be double to B. For A is nothing but the Line é 4 multiply’d by da. (6. 17.); and B is nothing but the Line cb multiply’d by the fame Line ad, or (whichis all one) be or fe. Wherefore (6. 15.) A: B:: ab: bc. 35. All Parallelograms which are between the fame Parallels (or which bave the fame Height) are as their Bafes. J fay the Parallelogram eb is ed SF J tothe Parallelogram bg :: as the ne Laye Bafe 4 b is to the Bale bc. For ha- 040) ving made the two prick'd Re@- ob € angles on the fame Bafes, thofe will be equal to the Parallelograms, (by 3. 14.) But thofe Rectangles are as their Bafes _ (by the Precedent). Wherefore the Parallelograms mt alfo be as their Bafes; That ised: bgs: abs C. 36. All Triangles (which have the fame Heights) or are between the fame Parallels, as are their Ba- fes; For they are Halves of Parallelograms (3. 8.) _ 37. When Triangles (as thofe in the following Figure) have their Bafes on one and the fame Line, — and their Verrices or Tops meeting in the famePoint: _ They are taken ro be between the fame Parallels, as ade and cde, and a de and bde (becaufe they bave. the fame perpendicular Height. ) ead PRO- |](https://iiif.wellcomecollection.org/image/b33009417_0104.jp2/full/800%2C/0/default.jpg)
