## 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 ... |

### From inside the book

Results 1-5 of 16

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 VERSED**SINE**of an arc is that part of the diameter which is between the**sine**and the arc . Thus BA is the ... Page 43

...

...

**half**120 ° , that is , to All the angles being equal , the sides are equal , and therefore AS , the chord of 60 ° , is equal to CS the radius . 3. Let AR be an arc of 45 ° . AD will be its**tangent**, and the angle ACD subtended by the ... Page 46

...

...

**tangent**is the logarithm of the natural**tangent**, & c . 103. One circumstance , however , is to be attended to ...**half**of 90 ; if any given angle within the quadrant is greater than 45 ° , its * Or the tables may be supposed to be ... Page 68

...

...

**tangent of half**the sum of the oppo- site angles , To the**tangent of half**their difference . Thus the sum of AB and AC ( Fig . 25. ) is to their differ- ence ; as the**tangent of half**the sum of the angles ACB and ABC , to the**tangent**... Page 69

...

...

**tangent of half**the sum of the opposite angles ; EB the**tangent of half**their difference . But , by similar triangles , CG : DB :: GE : EB Q. E. D. THEOREM III . 145. If upon the longest side of a triangle , a perpendicu- lar be drawn ...### 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.