Image from page 20 of “Trigonometria” (1658)

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Image from page 20 of “Trigonometria” (1658)
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Identifier: trigonometria00newt
Title: Trigonometria
Year: 1658 (1650s)
Authors: Newton, J.
Subjects:
Publisher:
Contributing Library: The Computer Museum Archive
Digitizing Sponsor: Gordon Bell

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. In the preceding Diagram, let H G be the tangent of the arch E G, and CK.the tangent of the arch C E, or complement of E G ; the triangles A L H and A C K are like,becaufe of their right angles at L and C, and their cbmmo n angle at A. Therefore as A L, c-qual to H G, the tangent of the arch EG, is to L H equal to A G Radius: Co is A C Radius,to C K the tangent ot C E, or complement of the arch E G, as was to be proved. Confettary. Therefore the tangent of an arch being given, the tangent complement is alfo given by Di-vHion onely. For if the re&angie of AC and A L, that is, the fquare of Radius, be dividedby M G, the quotient (hall be CK, the tangent complement of E G. aS Two unequal arches being propofed, each lefie then a Quadrant, the fumme of theirtangents is to their difference, as the •fine of their fumme, to the fine of their difference. Demowfirat ion. Let the given arches be H D and DB,from the center A draw AD> and through the point D draw irkdndmeina MnUnniA lU

Text Appearing After Image:
draw CF : let A H be prolonged toF,and A B to C, and the arch D S equalto D B ; let A S be prolonged to E, anddraw B S to G, then is B L the fine ofB H, and S K the fine of S H, and B Gparallel to C F : and therefore, CF.FE::BG.GS.And becaufe the triangles B G L andS G K are like, therefore BG.GS::BL.SK. And therefore alfo, As C F, thefumme of the tangents, is to F E, thedifference; fo is B L the fine of thefumme, to S K, the fine of the diffe-rence. Of the quantity of Right lines drawn through the Circle. 2 9 The right lines drawn through the circle, whofe quantity we are to define, a re fuch acut the circle, and are called Secants. 30 The fecanr of an arch is a right line drawn the term of an arch, to the tangent-line, andagreeth to the arch of the circle cut thereby, and to the complement of that arch to a femi-circle. Thus (in the Figure of the 2 5f/>.hercof) the fecant AH is drawn through the term ofthe arch E G: to the tangent H G, and agreeth both to the arch E G, and to the

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Image from page 172 of “Trigonometria” (1658)
Computer
Image by Internet Archive Book Images
Identifier: trigonometria00newt
Title: Trigonometria
Year: 1658 (1650s)
Authors: Newton, J.
Subjects:
Publisher:
Contributing Library: The Computer Museum Archive
Digitizing Sponsor: Gordon Bell

View Book Page: Book Viewer
About This Book: Catalog Entry
View All Images: All Images From Book

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Text Appearing Before Image:
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Note About Images
Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability – coloration and appearance of these illustrations may not perfectly resemble the original work.