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added algebraic alternate angle ABC appears Arithmetic base binomial bisected Book called centre ciphers circle circumference coefficient coincide common consequently contained cube root decimal denominator described diameter difference divided divisor double draw drawn equal equation equivalent example expressed extracting figure fore four fourth fraction given gives greater half Hence indices join latter less manner means meet method multiplied negative obtained parallel parallelogram perpendicular positive preceding PROBLEM PROP proportionals quotient raised ratio rectangle Reduce remaining represented Required respect result right angles root rule segment sides simple square square root straight line subtracted surd taken tangent THEOREM third Transp triangle twice units unknown quantity Wherefore whole
Side 172 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 170 - 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 169 - 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 127 - 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 169 - 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 162 - 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 140 - 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 107 - 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.