## 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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acute againſt alſo Altitude Arch Baſe becauſe Caſe Center Chap Chords Comp Compaſſes Compl Complement contained Courſe Declination Departure deſcribe Dial Diff Difference Difference of Longitude Diſtance double draw drawn Eaſt equal Example extend Extremes fall firſt flanked former given greater half half Sum half Tangent height Horizon Hour Hour-Lines Hypothenuſe laſt Latitude leſs Line meaſure Meridian middle Miles muſt North Numbers oblique angled oblique Circle oppoſite Parallel Perpendicular Place Plain Points Pole Port primitive Circle PROBLEM Proportion Quadrant Radius remains repreſent right Angles Rule Ruler ſame Scale Secant ſecond ſet ſhall Ship Side Side BC Sine South ſpherical Triangle Stile Sub-ſtile ſubtract Sun's Table Tangent Terms theſe third thoſe thro Triangle Triangle ABC Weſt

### Popular passages

Page 36 - 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 122 - 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 35 - 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 34 - 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 85 - ... 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 117 - TWo fides and an angle oppofite to one of them being given, To find the third fide and either of the other angles.

Page 36 - 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...