. Trigonometria. aineft jThen, As the Reft angle of the half fumme of the fides, and the difference between that halffumme, and thefide oppofiteto the anvle required. Is to the Reel: angle of the other two remainers. So is the fquare of Radius ; To e of the tangent of half the angle fought. DEMONS T %^A T 1 0 N. In the triangle BCD, let the fides. D B and D C, be produced to F and G, fo as that D F may be e-qual to half the fides D B, D € and C B , and equal f»DG, and let the angles at F and G be right-,upon the point H draw the periphery G V F, touching the fides D B and DC, being ex
. Trigonometria. aineft jThen, As the Reft angle of the half fumme of the fides, and the difference between that halffumme, and thefide oppofiteto the anvle required. Is to the Reel: angle of the other two remainers. So is the fquare of Radius ; To e of the tangent of half the angle fought. DEMONS T %^A T 1 0 N. In the triangle BCD, let the fides. D B and D C, be produced to F and G, fo as that D F may be e-qual to half the fides D B, D € and C B , and equal f»DG, and let the angles at F and G be right-,upon the point H draw the periphery G V F, touching the fides D B and DC, being extended to F andG. The fame arch muff of neceffuy touch the fide C B alfo in the point V , becanfe C V and V B, aretogether equal to CG and^^^bythe work. Now then upon the center^ defcribe the circle NOR,making R G and N F> equal to D C, then the difference between D G the half fumme ofthefides^and the fide C B i And the difference between D G the half fumme, and the fide DC is the right line 47 G-. Tngonometria Britannica UneQQ. or BN, to which feOB be equal, and the differencebetweenE) F the half fumme, and the fide D E // the right line B F, equal wCO, C R, or B V, alfo eqialto F H B. Therefore, As EN. N B :.: B F. F H , /?W ?ta rellangle mads of EN <*#^F His equal to the re3an<rle made of N B «u* B F. #« <w F D. N D : : H F. EN, And as HFw£N, /o tf f he reft angle of HV and EN to the fqttare of EN, whofe root u the fide E N, or the Radius of the circle NO K; and now if you dedntt the fide D C oppofite to the angle at B, from D G the halffumme of the fides, the difference isCG, equal to N B, then in the triangle END; i;ND. Rad .• : N E f D. Firft,then, : : BN inF B. E Nfquare, and multiplying the
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Keywords: ., bookcentury1600, bookdecade1650, bookidtrigonometri, bookyear1658
