The Doctrine of Plain and Spherical Trigonometry: With Its Application and Use in the Following Parts of Mathematicks : Viz. I. Navigation in All Its Kinds ; as Plain Sailing, Mercator's Sailing, Middle Latitude, and Parallel Sailing, II. Astronomy, Wherein All the Problems Relation to the Doctrine of the Sphere are Solved, III. Projection of the Sphere in Plano, IV. Geography, V. Fortification, VI. Mensuration of Heights and Distances, Both Accessible and Inaccessible, VII. Dialling, Arithmetical and Intrumental, on All Sorts of Planes

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J. Darby, 1725 - Astronomy - 479 pages
 

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Page 34 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 120 - As the cosine of half the sum of the two sides is to the cosine of half their difference, so is the cotangent of half the contained angle to the tangent of half the sum of the other two angles.
Page 33 - FG 5 that is in Words, half the Sum of the Legs, Is to half their Difference, As the Tangent of half the Sum of the oppofite Angles, Is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum...
Page 32 - IN a plain triangle, the fum of any two fides is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference.
Page 83 - ... to make the heart of a spectator ache, who knows the effect and the absurdity of it, to see five horses at length drawing a plough, and that perhaps upon a rich loam, where the force required is not more than 3 cwt. He cannot but think that in such cases the first horse draws the second, the second the third, the third the fourth, the fourth the fifth, and the fifth the plough, and that in fact the principal part of the draught lies upon the first horse...
Page 115 - TWo fides and an angle oppofite to one of them being given, To find the third fide and either of the other angles.
Page 34 - FG ; that is in Words, half the Sum of the Legs is to half their Difference, as the Tangent of half the Sum of the oppofite Angles is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs is to their Difference, as the Tangent of half the Sum of the Angles oppofice is to the Tangent of half their Difference. j. ED Axiom IV. -4. The Bale, or greateu Side of any $• Plane Triangle is to the Sum of fs...
Page 478 - Extraction of the Square and Cube Roots. And alfo the Multiplication of Feet and Inches, commonly call'd Crofs-Multiplication.
Page 478 - ... that Court and Country. The Eighth Edition. With the Addition of a Letter of the State of Spain, as it was in the Year 1700. By ad Enelifo Gentleman. In Three Parts. The Compleat Meafurer ; or, the whole Art of Meafuring
Page 478 - The fecond Part teaching to meafure all forts of Superficies and Solids, by Decimals, by Crofs- Multiplication, and by Scale and Compafles. Alfo the Works of the feveral Artificers relating to Building-, and the Meafuring of Board and Timber : Shewing the common Errors.

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