## 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

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**trigonometrical**calculations are founded , the proportion between the parts of the given tri- angle , and a similar one formed from the sines , tangents , & c . in the**tables**. The solutions of oblique angled triangles are made by the ... Page

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**Trigonometrical Tables**37 45 III . Solutions of Right angled Triangles 52 Solutions of Oblique angled Triangles 67 Geometrical Construction of Triangles 78 VI . Description and use of Gunter's Scale 84 VII . Trigonometrical Analysis ... Page 44

... ABH and ABF are similar . ( Euc . 8. 6. ) Therefore , AH : AB :: AB : AF . That is , the diameter is to the chord , as the chord to the versed sine . * * Sec note E. V SECTION II .. THE

... ABH and ABF are similar . ( Euc . 8. 6. ) Therefore , AH : AB :: AB : AF . That is , the diameter is to the chord , as the chord to the versed sine . * * Sec note E. V SECTION II .. THE

**TRIGONOMETRICAL TABLES**. ART . 98. 41 TRIGONOMETRY . Page 45

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**TRIGONOMETRICAL TABLES**. ART . 98. To facilitate the operations in trigonometry , the sine , tangent , secant , & c . have been calculated , for every degree and minute , and , in some instances , for ev- ery second , of a quadrant ... Page 46

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**tables**here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined in arts . 82 , 83 , & c . By means of them , the angles and sides of triangles may be accurately ...### 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.