## 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 11

Page 46

...

...

**radius**, as they extend from the centre , to a point without the**circle**. 102. The numbers in the**tables**here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined ... Page 53

... radius to which the trigono- metrical tables are adapted . In the first place , let the base of the triangle be equal to the

... radius to which the trigono- metrical tables are adapted . In the first place , let the base of the triangle be equal to the

**tabular radius**. Then , if a circle be described , with this radius , about the angle C as a centre , DA will ... Page 54

...

...

**tabular radius**, will have its other two sides found among the sines and cosines . Thus if the quad- rant AH ( Fig ... radius of the tables . But for determining the parts of triangles which have not any of their sides equal to the ... Page 55

... radius . Proportions are then stated , between these lines , and the

... radius . Proportions are then stated , between these lines , and the

**tabular radius**, sine , tangent , & c . 120. A line is said to be made radius , when a circle is de- scribed , or supposed to be described , whose semidiameter is ... Page 56

...

...

**radius**, as in Fig . 14 , the perpendicular be will be the**tabular**sine of the angle at a ; and the perpendicular BC will be a sine of the equal angle A , in a**circle**of which AC is**radius**. If the base in each triangle be made**radius**...### 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.