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 |
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Strona x
... less time , and with far less difficulty and labour , than Simson's or any other edition of Euclid's Ele- ments of Geometry . Some teachers would perhaps be satisfied with the element- ary propositions of trigonometry , and would be ...
... less time , and with far less difficulty and labour , than Simson's or any other edition of Euclid's Ele- ments of Geometry . Some teachers would perhaps be satisfied with the element- ary propositions of trigonometry , and would be ...
Strona 3
... less intricate than frac- tions . LEMMA II . 7. ALL angles are to one another as their arcs directly ; and their radii inversely . Fig . to Art . 1 . The angle ABC : 4 right angles :: the arc AC circumfe- rence ADEFA ( 1. ) , therefore ...
... less intricate than frac- tions . LEMMA II . 7. ALL angles are to one another as their arcs directly ; and their radii inversely . Fig . to Art . 1 . The angle ABC : 4 right angles :: the arc AC circumfe- rence ADEFA ( 1. ) , therefore ...
Strona 7
... 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 diameter HL , then CF - BI . But BI , HK , CK , are respectively the sine ...
... 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 diameter HL , then CF - BI . But BI , HK , CK , are respectively the sine ...
Strona 8
... less sine , tangent , and secant . 34. Let the arcs Ab and AB be supplements to each other , namely , Ab greater , and AB less than a quadrant ; then will their sines bf and BF be equal . Because Ab + AB = 180 ° = Ab + bD , the arc AB ...
... less sine , tangent , and secant . 34. Let the arcs Ab and AB be supplements to each other , namely , Ab greater , and AB less than a quadrant ; then will their sines bf and BF be equal . Because Ab + AB = 180 ° = Ab + bD , the arc AB ...
Strona 10
... less than a quadrant be- ing equal to the difference between the radius and the cosine , the versed sine of 60 degrees - radius - cosine of 60 degrees = radius - half radius = half radius . 46. On the diameter AD describe a semicircle ...
... less than a quadrant be- ing equal to the difference between the radius and the cosine , the versed sine of 60 degrees - radius - cosine of 60 degrees = radius - half radius = half radius . 46. On the diameter AD describe a semicircle ...
Kluczowe wyrazy i wyrażenia
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
Popularne fragmenty
Strona 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.
Strona 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.
Strona 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.
Strona 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.
Strona 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...
Strona 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.