## A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of the Nature and Use of Logarithms. Being the Second Part of A Course of Mathematics, Adapted to the Method of Instruction in the American Colleges ... |

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Page 40

... sine is half the chord of double the arc . The sine BG is half PG , which is the chord of the arc PAG , double the arc AG . 83. The

... sine is half the chord of double the arc . The sine BG is half PG , which is the chord of the arc PAG , double the arc AG . 83. The

**VERSED SINE**of an arc is that part of the diameter which is between the sine and the arc . Thus BA is the ... Page 41

... sine of HCG . ( Art . 82. ) It is , therefore , the cosine of GCA . On the other hand GB is the sine of GCA , and ...

... sine of HCG . ( Art . 82. ) It is , therefore , the cosine of GCA . On the other hand GB is the sine of GCA , and ...

**versed sine**of an angle is not the same , as that of its supplement . The**versed sine**of an acute angle is equal ... Page 44

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**versed sine**of the arc . Let ADB ( Fig . 6. ) be an arc , of which AB is the chord , BF the sine , and AF the**versed sine**. The angle ABH is a right angle , ( Euc . 31. 3. ) and the triangles ABH and ABF are similar . ( Euc . 8. 6 ... Page 94

... sinę . R2 3. Sin : R :: R : cosec , that is , Cosec = sin The cosecant , therefore , must have the same sign as the sine . The

... sinę . R2 3. Sin : R :: R : cosec , that is , Cosec = sin The cosecant , therefore , must have the same sign as the sine . The

**versed sine**, as it is measured from A , in one direction only , is invariably positive . 197. The tangent AT ... Page 113

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**versed sine**of the supplement of twice a given arc , is equal to twice the square of the cosine of the arc . And the product of the sine of an arc , into the**versed sine**of the supplement of twice the arc , is equal to the product of ...### Other editions - View all

### Common terms and phrases

acute angle added angle ACB arithmetical complement arithmetical progression b+sin base calculation centre circle cosecant Cosine Cotangent Tangent decimal degrees and minutes divided division divisor equal to radius equation errour exponents extend find the angles find the logarithm fraction geometrical progression given angle given number given side Given the angle gles greater half the sum hypothenuse JEREMIAH DAY length less line of chords line of numbers lines of sines loga logarithmic sine logarithmic TANGENT metical Mult multiplied natural number natural sines number of degrees opposite angles perpendicular positive proportion quadrant quotient radix right angled triangle rithms root secant similar triangles sine of 30 sines and cosines slider square subtracting tables tabular radius tabular sine tangent of half theorem transverse distance triangle ABC trigonometrical tables Trigonometry versed sine vulgar fraction

### Popular passages

Page 68 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.

Page 105 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.

Page 49 - ... at the head of the column, take the degrees at the top of the table, and the minutes on the left; but if the title be at the foot of the column, take the degrees at the bottom, and the minutes on the right.

Page 39 - With these the learner should make himself perfectly familiar. 82. The SINE of an arc is a straight line drawn from one end of the arc, perpendicular to a diameter which passes through the other end. Thus BG (Fig.

Page 116 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 37 - The periphery of every circle, whether great or small, is supposed to be divided into 360 equal parts called degrees, each degree into 60 minutes, each minute into 60 seconds, each second into 60 thirds, &c., marked with the characters °, ', ", '", &c. Thus, 32° 24...

Page 72 - ... angle. The third angle is found by subtracting the sum of the other two from 180° ; and the third side is found as in Case I.