The svrveyor in foure bookes / By Aaron Rathborne.

  • Aaron Rathborne
Date:
1616
Catalogue details

Licence: Public Domain Mark

Credit: The svrveyor in foure bookes / By Aaron Rathborne. Source: Wellcome Collection.

    102/252 page 88
    89 _ Lhe Surueyors Part.2. | ? len ange g Prospreme LXX, | a | fn The Semidiameter and Arch line of a Sector of a Circle given tofindthe § st f Area, ? | pe Semidiameteris D, G. or D.B, and the: arch line B.C. and itisrequi- | “red to finde the: Area. Multiply the Semidiameter.7. by halfethe i? arch line B.C. 5. 3. the Product is 38. :.forthe Area required, Tues 9 ™ OR. 64. i fro ee a LX XI, | [5 theformer Diagram, let B.C: D. bethe Seftor ofa Circle, whofe I G Any Segment or part of aGircle being ginen, to finde the fuperficall t content thereof. ‘PEN the former Diagram, let A. F. B. E. be the Segment ofa Circle, the Lok whereofisrequired. By the34. Pros. finde out the Centre, ‘and then draw the-lines D. A,and D.B. arid.catt vp the whole Figuté A. F.B.D, as in thelaft Probleme which will be 38.4. then finde the fu- perficiall content ofthe Triangle,A.B.D. bythe 4t, Pxosswhichisa4®. and deduct the fame out ofthe whole content 38.4 refteth 14; for the fispers ficiall content ofthe giuen. Segment as was required. : tums? By thisrule (obferned with difcretion) may all manner of Segments of parts ofa Circle, whether greater or lefler then a Semicircle, be eafily meas {ured without farther inftruCtion. yi Notes But here isto bee noted, that the precedent rules concerning the menfiration of — _ Circles, and their fenzrall parts, arenot exactly true: for that the proportion bene tweene the Diameter and circumference is irrational and the [quaring of a GiF- ' ele or the meanes thereof (other then mechanically) not yet difconeredor fouwd outs yet of fuch{ufcient precifene(fe as no notable or apparant error cap be madeor found im the conclufions thereby wrought. Prosprems LXXIE An irregular plotte or Figure being ginen, to finde the Area or fu ¥ perficiall content thereof. Megalo 7 Et A.B. C. D,E.F.G. H. I. be an irregular plottedr Figure,whofe § © fuperficiall- capacitie is required. Reduce the fame into 4s many Trapeziasas it will containe,“as firft the Trapezium A.B. C.D. Se- condly, A.DE F. Thirdly, A. F,G.I. and there remaineth the Trian- gle, I. G.H. In which three Trapezias draw the Diagonals B' D, D F.and FI.
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