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 2
... measured in the former case is to the magni- tude of the quantity to be measured in the latter case . 6. Since then the whole circumference of a circle consists of 360 degrees , a right angle will be 90 degrees , two right an- gles ...
... measured in the former case is to the magni- tude of the quantity to be measured in the latter case . 6. Since then the whole circumference of a circle consists of 360 degrees , a right angle will be 90 degrees , two right an- gles ...
Page 6
... measured by that arc . 17. DEF . 5. The versed sine of an arc is that part of the diameter passing through the beginning of the arc which is in- tercepted between the beginning of the arc and the right sine . Thus , AF is the versed ...
... measured by that arc . 17. DEF . 5. The versed sine of an arc is that part of the diameter passing through the beginning of the arc which is in- tercepted between the beginning of the arc and the right sine . Thus , AF is the versed ...
Page 32
... measured on the same scale of equal parts , will be 199.5 and 156. The angle C = 90 ^ -51 ° 19 ′ = 38 41 . By Calculation . Angle C = 90-51 ° 19 ′ = 38 ° 41 ′ : Radius : tan . A :: AB : BC . R : tan . 51 ° 19 ′ :: 125 : BC . Cos . A or ...
... measured on the same scale of equal parts , will be 199.5 and 156. The angle C = 90 ^ -51 ° 19 ′ = 38 41 . By Calculation . Angle C = 90-51 ° 19 ′ = 38 ° 41 ′ : Radius : tan . A :: AB : BC . R : tan . 51 ° 19 ′ :: 125 : BC . Cos . A or ...
Page 34
... measured on the line of numbers is 332 , and the angles A and C measured on the scale of chords , or with a protractor , are 53 ° 8 ' and 36 ° 53 ′ nearly . By Calculation . AC : AB :: R : sine C or cos . A. 415 : 249 :: R : sine C ...
... measured on the line of numbers is 332 , and the angles A and C measured on the scale of chords , or with a protractor , are 53 ° 8 ' and 36 ° 53 ′ nearly . By Calculation . AC : AB :: R : sine C or cos . A. 415 : 249 :: R : sine C ...
Page 37
... scale of chords make the angle A = 49 ° 25 ' , and the an- gle B = 66 ° 47 ' . Draw AC and BC meeting each other in C. Then AC and BC measured by the scale PLANE TRIGONOMETRY . 37 Solution of the Cases of Oblique-angled Triangles.
... scale of chords make the angle A = 49 ° 25 ' , and the an- gle B = 66 ° 47 ' . Draw AC and BC meeting each other in C. Then AC and BC measured by the scale PLANE TRIGONOMETRY . 37 Solution of the Cases of Oblique-angled Triangles.
Common terms and phrases
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc AC arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest formulæ 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 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.