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 BonnycastleF. Nichols, 1811 - 128 من الصفحات |
من داخل الكتاب
النتائج 1-5 من 55
الصفحة ix
... cosines of arcs , " which ( says professor Playfair ) are the foundation of those applica- tions of trigonometry lately introduced , with so much advan- tage , into the higher geometry , " are extracted from Playfair's Elements of ...
... cosines of arcs , " which ( says professor Playfair ) are the foundation of those applica- tions of trigonometry lately introduced , with so much advan- tage , into the higher geometry , " are extracted from Playfair's Elements of ...
الصفحة 6
... cosine of an arc is the part of the diame ter passing through the beginning of the arc which is inter- cepted between the centre and the sine . Thus , CF is the co- sine of the arc AB , or of the angle ACB ; and Cf is the cosine of the ...
... cosine of an arc is the part of the diame ter passing through the beginning of the arc which is inter- cepted between the centre and the sine . Thus , CF is the co- sine of the arc AB , or of the angle ACB ; and Cf is the cosine of the ...
الصفحة 7
... cosine , cotangent , and cosecant of an arc under 90 degrees , or of an angle less than a right an- gle , are respectively equal to the sine , tangent , and secant of the complement of that arc or angle . Draw BI perpendicular to the ...
... cosine , cotangent , and cosecant of an arc under 90 degrees , or of an angle less than a right an- gle , are respectively equal to the sine , tangent , and secant of the complement of that arc or angle . Draw BI perpendicular to the ...
الصفحة 8
... cosine of no degrees is radius , and the cosine of 90 degrees is 0 . 31. The versed sine of 90 degrees is radius , and the versed sine of 180 degrees is the diameter . 32. Universally , the versed sine is always either the sum or the ...
... cosine of no degrees is radius , and the cosine of 90 degrees is 0 . 31. The versed sine of 90 degrees is radius , and the versed sine of 180 degrees is the diameter . 32. Universally , the versed sine is always either the sum or the ...
الصفحة 9
... cosine , tangent , and secant of an arc ter- minating in the fourth quadrant LA , will be the same as those of an ... Cosine CF : sine BF :: radius CA : tangent TA . 2. Cosine CF : radius CB :: radius CA = CB : secant CT . 3. Sine BF ...
... cosine , tangent , and secant of an arc ter- minating in the fourth quadrant LA , will be the same as those of an ... Cosine CF : sine BF :: radius CA : tangent TA . 2. Cosine CF : radius CB :: radius CA = CB : secant CT . 3. Sine BF ...
عبارات ومصطلحات مألوفة
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
مقاطع مشهورة
الصفحة 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.
الصفحة 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.
الصفحة 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.
الصفحة 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.
الصفحة 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...
الصفحة 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.