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added Algebra appears apply base becomes called centre changed chord circle circumference co-sine common consequently contained demonstration described diameter difference distance divided division draw drawn equal equation Euclid evidently EXAMPLES.-1 expressed extremes feet figure former four fourth Geometry given greater half Hence idea increased join known latter length less likewise logarithms magnitude manner means measure meet method multiplied namely opposite parallel perpendicular placed powers problem progression Prop proportionals proposed proposition quadrant quantities quotient radius ratio remaining respectively result right angles roots rule scale shewn sides signs similar sine solidity square straight line substituted subtract taken tangent theor theorems third triangle whence wherefore whole
Page 293 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Page 249 - If two triangles have two sides of the one equal to two sides of the...
Page 261 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 60 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 365 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. 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 246 - But things which are equal to the same are equal to one another...
Page 270 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Page 174 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of
Page 283 - II. Two magnitudes are said to be reciprocally proportional to two others, when one of the first is to one of the other magnitudes as the remaining one of the last two is to the remaining one of the first.
Page 286 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.