## Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |

### From inside the book

Page 9

Q : E. D. THEOREM V. In any plane triangle , it will be , as the sum of any two sides

Q : E. D. THEOREM V. In any plane triangle , it will be , as the sum of any two sides

**is to their difference , so is the tangent of half the sum of**the two opposite angles , to the tangent of half their difference . Page 32

As the sum of the sines of two unequal arches

As the sum of the sines of two unequal arches

**is to their difference , so is the tangent of half the sum of**those arches to the tangent of half their difference : and , as the sum of the co - sines is to their difference , so is the co ...### What people are saying - Write a review

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### Common terms and phrases

added arch base called centre circle co-s co-sine AC co-tang common Comp complement consequently COROLLARY describe the circle diameter difference distance draw drawn equal evident excess extremes follows given angle given point gives greater half the difference half the sum Hence hypothenuse inclination intercepted intersect join known less line of measures logarithm manifest meeting minute Moreover oblique opposite parallel passing perpendicular plane of projection plane triangle ABC pole primitive PROB produced projecting point PROP proportion proposed proposition radius rectangle respectively right line RULE secant semi-tangents sides similar sine sine AC sphere supposed tang tangent of half Theor THEOREM triangle ABC fig Trigonometry vertical angle whence

### Popular passages

Page 2 - An Act for the Encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies during the time* therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.

Page 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...

Page 9 - Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them.

Page 5 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.

Page 7 - Canon, is a table showing the length of the sine, tangent, and secant, to every degree and minute of the quadrant, with respect to the radius, which is expressed by unity or 1, with any number of ciphers.

Page 32 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Page 38 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.

Page 89 - ... projection is that of a meridian, or one parallel thereto, and the point of sight is assumed at an infinite distance on a line normal to the plane of projection and passing through the center of the sphere. A circle which is parallel to the plane of projection is projected into an equal circle, a circle perpendicular to the plane of projection is projected into a right line equal in length to the diameter of the projected circle; a circle in any other position is projected into an ellipse, whose...

Page 48 - The sum of the logarithms of any two numbers is equal to the logarithm of their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.

Page 38 - The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT.