A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and Bonnycastle |
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Page iii
... Calculation Observations preparatory to the Practical Solution of Plane Triangles Solution of the Cases of Right - angled Triangles Solution of the Cases of Oblique - angled Triangles Mensuration of Heights and Distances 5 7 12 19 27 30 ...
... Calculation Observations preparatory to the Practical Solution of Plane Triangles Solution of the Cases of Right - angled Triangles Solution of the Cases of Oblique - angled Triangles Mensuration of Heights and Distances 5 7 12 19 27 30 ...
Page xi
... calculations , which will promote his progress in the study of navigation , physical astronomy , and other branches of mixed mathematics . In some articles , algebra has been applied to facilitate and shorten the demonstrations , which ...
... calculations , which will promote his progress in the study of navigation , physical astronomy , and other branches of mixed mathematics . In some articles , algebra has been applied to facilitate and shorten the demonstrations , which ...
Page 5
... calculation , the practical solution of the cases of rectilinear triangles , and the mensuration of heights and distances ; the third contains the changes of the signs of trigonometrical lines , the investigation of some theorems ne ...
... calculation , the practical solution of the cases of rectilinear triangles , and the mensuration of heights and distances ; the third contains the changes of the signs of trigonometrical lines , the investigation of some theorems ne ...
Page 19
... CALCULATION . 67. THE general problem which trigonometry proposes to resolve is this . In any plane triangle , of the three sides and the three angles , three parts being given , one of which is a side , to find any of the other three ...
... CALCULATION . 67. THE general problem which trigonometry proposes to resolve is this . In any plane triangle , of the three sides and the three angles , three parts being given , one of which is a side , to find any of the other three ...
Page 20
... calculation it is usual to divide the general problem into two problems , according as the proposed triangle is right - angled or oblique - angled . A right - angled triangle consists of three variable parts , the three sides and the ...
... calculation it is usual to divide the general problem into two problems , according as the proposed triangle is right - angled or oblique - angled . A right - angled triangle consists of three variable parts , the three sides and the ...
Common terms and phrases
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest geometry Given the side greater than 90 half the sum half their difference height Hence hypothenuse AC included angle less than 90 logarithmic sines mathematics measured mechanical philosophy negative opposite angle perp perpendicular plane triangle plane trigonometry PROP propositions quadrant AH quantity right-angled spherical triangle right-angled triangle Scholium secant side AB side AC sides and angles sine a sine sine and cosine sine² sines and tangents solution spherical angle spherical triangle ABC spherical trigonometry supplement tables tangent of half theorems third side three angles three sides triangle are given trigono versed sine yards
Popular passages
Page 12 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page ix - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 23 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.
Page 13 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.
Page 87 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Page 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.