## A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and Bonnycastle |

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90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest geometry Given the side greater than 90 half the sum half their difference height Hence hypothenuse AC included angle less than 90 logarithmic sines mathematics measured mechanical philosophy negative opposite angle perp perpendicular plane triangle plane trigonometry PROP propositions quadrant AH quantity right-angled spherical triangle right-angled triangle Scholium secant side AC sides and angles sine a sine sine and cosine sine2 sines and tangents small arc solution spherical angle spherical triangle ABC spherical trigonometry supplement tables tangent of half theorems third side three angles three sides triangle are given trigono versed sine Xcos yards

### Popular passages

Page iii - 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 times therein mentioned." And also to the act, entitled " An Act supplementary to an Act, entitled, " 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...

Page iii - IDE, of the said District, hath deposited in this office, the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " Inductive Grammar, designed for beginners. By an Instructer." In conformity to the act of the Congress of the United States...

Page 18 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.

Page 3 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.

Page 29 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.

Page 19 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.

Page 93 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...

Page 80 - The sum of any two sides is greater than the third side, and their difference is less than the third side.

Page iii - An Act supplementary to an Act, entitled, " 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 times therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.

Page iii - Adapted to the use of Students. Extracted mostly from similar " works of Ludlam, Playfair, Vince, and Bonnycastle. By F. Nichols, " Member of the Literary and Philosophical Society of Manchester, " and of the American Philosophical Society.