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added Algebra appears apply axis base becomes called centre chord circle circumference co-sine common compasses consequently contained curve definition demonstration described diameter difference distance divided division draw drawn equal equation Euclid evidently EXAMPLES.-1 expressed Extend figure former four fourth Geometry given greater half Hence idea join known latter length less likewise logarithms manner means measure meet method multiplied obtained opposite parallel perpendicular placed plane powers preceding problem Prop proportionals proposed proposition proved quadrant quantities quotient radius ratio remaining respectively result right angles roots rule scale shewn sides similar sine square straight line substituted subtracted taken tangent theor third triangle whence wherefore whole
Page 294 - 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 263 - 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 62 - 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 369 - 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 248 - But things which are equal to the same are equal to one another...
Page 272 - 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 176 - 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 285 - 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.