Page:Elements of philosophy, the first section, concerning body (IA b30335838).pdf/213

Part3. MOTIONS & MAGNIfUDtS. 183 andcoiifequcmlyjwiih the magnitudes of their CompleteFiouresAnd they will be‘found to be as I have fet them down in the foh lowing Tables; in which I compare a Parallelogram with three fided Figures; and firft with a ftraight lined triangle,made by the bale of the Parallelogram continually decrealing in fuch manner-; that the altitudes be alwayes in proportion to one another as the bafes arc, and fo the triangle will be equal to its Complement •, or the proportions of thealdtudes and bafes wil be as i to i,and then the triangle will be half the ParaUelogram., Secondly, with that which rs made by the continual decreafino-of the bafes m fubduplicate proportion to that of the altitudes;and fo the Deficient Figure will be double to its Complement, and to the ara e ogramas 2 to 3. Then, with that, where the proportion ol the altitudes is triplicate to that of the bafes; and then the De¬ ficient Figure will be triple to its Complement, and to the ParalWogram as 3 to 4. Alfothe proportion of the altitudes to that of the bafes may be as 3 to 2; and then the Deficient Figure will be to its Complement as 3 to 2, & to the Parallelogram as 3 to s;and lo forwards according as more mean proportionals are taken,or as the proportions are more multiplyed, as may be feen in the follow¬ ing Table For example, if the bafes decreafe fo, that the pro¬ portion of the altitudes to that of the bafes be alwayes ass to 2, and it be demanded what proportion the Figure made has to the Parallelogram, which is fuppofed to be Unity; then, feeing that

where the proportion is taken five times, there muft be four . eans 5 b} the Table among!! the three-fided figures ol four Means, and feeing the proportion was as 5 to 2, look in the uppermoil row for the number 2, and defeending in the 2d Coiumne till you meet with that three-fided Figure,you will finde 4; which mews that the Deficient Figure is to the Parallelogram as 4 to 1, or as 5 to 7.

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