# A Mathematical Manual; Containing Tables of Logarithms for Numbers, Sines, and Tangents. with the Manifold Use Thereof Briefly Explained and Applied in Arithmetick, Geometry, Astronomy, Geography, Surveying, Navigation, Dialling, Gunnery, and Gauging

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1677 Excerpt: ...to do it at two Operations, wirnout finding the length of the Perpendicular Z R, work thus. A First, As the Radius or Sine of Z R P, ' fotbercfmeof ZPR-q j 1 'So the Tangent f Z P, q lo the tangent of the Ai P R..., j;' 3-Secondly, Secondly, At the Cosine of P R, qfethe Cosine of ZP: . '. So the Cofrne of RO, .q-Tothe Cosine of ZO. So the Height of the Sun at that distance from the Meridian will be about 40 dtg. haying that Declination. By this Propolition also, having the Complements of the Latitude of any two Places and their Difference of Longitude, which is the Angle at P, you may find their Distance, which is the Side Z . Likewise having the Complements of the Latitudes, or Declinations of any two Stars, and the Difference of their Longitudes or Right Ascensions for the Angle at P, you may rind their Distance, Which will be the SideZO. 1 But in letting fall this Perpendicular, sometimes it will fall without the Triangle, as here it doth within the Triangle: In that Cafe the Side of the Triangle must be continued, and so there will be two Rightangled Triangles, the ene included within the other.; . As for instance, F g.8. If the Triangle A B D were given, to let fall a Perpendicular from B, the Perpendicular B C falls without the Triangle, upon the Side A D prolonged toC; and so the two Right-angled fllbu.: i-'. f rianglci Triangles found hereby will be A C B and DCB: arid sq you may by the former Propositions find out the Side B D. Prop. 82. Case: o. Two Sides and the, Angle included being fyotien-i tt find either of the other Angles. As in the Triangle ZPO, Fig. J-knowing ZPSdeg. aOmin. and P qjod.om. and the Angle P31 . to find the: Angle at 0. First let fall the Perpendicular 2 R, ...This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed.

 Title : A Mathematical Manual; Containing Tables of Logarithms for Numbers, Sines, and Tangents. with the Manifold Use Thereof Briefly Explained and Applied in Arithmetick, Geometry, Astronomy, Geography, Surveying, Navigation, Dialling, Gunnery, and Gauging Author : Henry Phillippes Publisher : Rarebooksclub.com - 2012-05-18