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 σελίδες |
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Σελίδα iv
... Cos . 121 26 For Cot . read Cos . After the second of add the sine of Add Plate , fig . 4 . Articles which may be omitted . The following articles may be omitted , or deferred till the second reading of the book . Art . 46 , 47 , 63 to ...
... Cos . 121 26 For Cot . read Cos . After the second of add the sine of Add Plate , fig . 4 . Articles which may be omitted . The following articles may be omitted , or deferred till the second reading of the book . Art . 46 , 47 , 63 to ...
Σελίδα 5
... sine or right sine of any arc is a straight line drawn from the end of the arc perpendicular to the dia- meter passing through the beginning of the arc . From B demit BF perpendicular to AD , then BF is the sine of the arc AB , or of ...
... sine or right sine of any arc is a straight line drawn from the end of the arc perpendicular to the dia- meter passing through the beginning of the arc . From B demit BF perpendicular to AD , then BF is the sine of the arc AB , or of ...
Σελίδα 6
... sine . Thus , AF is the versed sine of the arc AB , or of the angle ACB ; and Af is the versed sine of the arc AHb , or of the angle ACb . 18. DEF . 6. The tangent of an arc is a straight line touch- ing the circle in the beginning of ...
... sine . Thus , AF is the versed sine of the arc AB , or of the angle ACB ; and Af is the versed sine of the arc AHb , or of the angle ACb . 18. DEF . 6. The tangent of an arc is a straight line touch- ing the circle in the beginning of ...
Σελίδα 7
... sine , tangent , and secant of the comple- ment of that arc or angle , whence they derive their names . Of the Properties and Relations of Trigonometrical Lines . 24. The sine , cosine , tangent , secant , & c . of any angle ACB , in a ...
... sine , tangent , and secant of the comple- ment of that arc or angle , whence they derive their names . Of the Properties and Relations of Trigonometrical Lines . 24. The sine , cosine , tangent , secant , & c . of any angle ACB , in a ...
Σελίδα 8
... sine of 90 degrees , or a quadrant , or a right angle , is equal to radius . This is manifest from an inspection of the figure . 28. The tangent of 45 degrees is radius . For then the angle ACT being half a ... sine 8 PLANE TRIGONOMETRY .
... sine of 90 degrees , or a quadrant , or a right angle , is equal to radius . This is manifest from an inspection of the figure . 28. The tangent of 45 degrees is radius . For then the angle ACT being half a ... sine 8 PLANE TRIGONOMETRY .
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.