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, Appollonius, 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:: 1734

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, Appollonius, 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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$Ifthe Line 42 be produced to e, it will be a new Diameter, and will make below two other Angles: | So that in the whole here will be four Angles; of which thofe two that touch only in the Angular G Point, as ac and ead; as alfo, 4ab and eac, are called Vertical, or Oppofite Angles. But thofe that | have one Leg common to both, as dab and bac; and bac and eac are called 47- joining or Contiguous Angles. | | 18. Thofe Angles, which (at equal Diftances from — the Angular Point) are fubtended by equal Arks, are alfo equal themfelves. Asif the Ark &c be pro- ved equa} to the Ark Ze, then will the Angle # ac be equal'to dae. : 3 nyt 19. The two Coatiguons Angles, taken together, are always equal to two Right ones. 3 For as the Line 2¢ is a Diameter, and therefore : cuts the Circle into two equal Parts,the two Arks, 4 D and bc, taken together, will be equal to a Semi- circle. Whereforethe two Angles, 44h and bac, together, will be equal to two Right ones, becaufe they compleat the whole Semi-circle, as two Right : ones do. (Art. 15.) TU 20, So that this Propofition is of univerfal Truth, That cue Richt Line, falling omanother, makes the Coutisuons dugtes(together) equal totwo Right ones. For ifthe Lines are Perpeuaicular to each other, as P44 is to dc; then ’tis plain the © pl /& Angles muft be Right (by the 15°) | /. And \if the Line fall obliquely, as” ] 7 _&adoth, then indeed the Angles ” “qa areumequals But aganuch 4s the®: Obtufe one 4 4 b exceeds one Right Angle, by fo much is the Acute one Dac exceeded by$

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