. Trigonometria. efore, As the s C into s i C E. s K into s \ K L:: fquare A x. fquare t \ Alio, As the s K iato s ~ K L. s C into s \ C E :: fquare A x. fquare ct \ B. This I aft variety is uf(tally ex pre fed thm. As the rectangle of the half fumme of the three fides,and the fine of the differenceof the bafe, and half fumme, To the quadrat of is the rectangle made of the fines of the difference of each containing fide, and the halffumme, To the fquare of the tangent of half the angle inquired. Which is in effect thefame with the former. PROPOS ITION. II. In all obliqttangled
. Trigonometria. efore, As the s C into s i C E. s K into s \ K L:: fquare A x. fquare t \ Alio, As the s K iato s ~ K L. s C into s \ C E :: fquare A x. fquare ct \ B. This I aft variety is uf(tally ex pre fed thm. As the rectangle of the half fumme of the three fides,and the fine of the differenceof the bafe, and half fumme, To the quadrat of is the rectangle made of the fines of the difference of each containing fide, and the halffumme, To the fquare of the tangent of half the angle inquired. Which is in effect thefame with the former. PROPOS ITION. II. In all obliqttangled Spherical triangles, the fumme ofwhofe angles at the bafe , are lelfe then a femi-cir-cle, As the fine of the fumme of the angles at the bafe, is to the fine oft heir difference ; So is the tangentof halfthe bafey to the tangent of the half differenceof the fegments of the bafe, * DEMONSTRATION. la the Obliquangled fpherical triangle A B E, or A B C, in which the angles at the bafe are Trigonometria Britanmca. 67. •,r are acute,and A C B obwfe,!et the fide A C be eqal to A E, and from the angle at A let fall theperpendicular A D, then are the triangles A C D. and A D E equilateral, and cqiti-angled,and C D equal to D E, and in the triangle A B E,the bafe is B E, and B D, and D E, the fummeof the fegments, and by the 6 cdnfedt. chap. ■>. s D E. jB D:: t B t E. Now then in the plain triangle F G H . let H F rc-prefentthe tangent of the angle at B , an J F G thetangent of the angle at E, and let the angle G F H beequal to the complement or B E to a femi-circle,then are the angles at G and H togetherv equal to the gbafe B E, and sH. s G :: t G F. t F H, h the 3 Prop,of Tlam Triangles, and therefore the arch BD is equalto the angle at H, and the arch DE to the angle at G,and bythe 4 Prop, of T>lain Triangles. &As the fummeof the fides G F, and F H, it to their difference ; fo is thetangent of the halffumme of the angles at G and H, to thetangent of half their difference. A
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Keywords: ., bookcentury1600, bookdecade1650, bookidtrigonometri, bookyear1658
