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added algebraic quantities angle ABC angle ACB angle BAC angle EBA annex Arithmetic base binomial Binomial Theorem bisected called centre ciphers circle circumference coefficient consequently continued fraction counters cube root decimal fraction Denary denominator difference digits divided dividend divisor drawn equal angles equation equiangular example expressed exterior angle figure find the values fore fourth given number greater greatest common measure Hence improper fraction join least common multiple less lowest terms manner merator minuend multiplied number of terms opposite angle parallel parallelogram perpendicular preceding prefixed PROP proportionals Q. E. D. Cor quotient ratio rectangle contained Reduce remaining angle Required the sum right angles rule scale Scholium segment sides square root subtracted subtrahend surd tangent THEOREM third Transp triangle ABC units unity unknown quantity vulgar fraction Wherefore whole number
Side 198 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 196 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...
Side 195 - 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.
Side 153 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other.
Side 195 - C to the remaining angle at F. For, if the angles ABC, DEF be not equal, one of them is greater than the other : Let ABC be the greater, and at the point B, in the straight line AB, make the angle ABG equal to the angle (23.
Side 188 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on GEOMETRY.
Side 166 - EK, because EH is less than EK ; therefore the square of BH is greater than the square of FK, and the straight line BH greater than FK, and therefore BC is greater than FG.
Side 133 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.