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Side 205
... ratio , and the ratio of the second to the third is equal to the second ratio , and so on , then the first of the set is said to have to the last the ratio compounded of the original ratios . Obs . From these definitions it follows , by ...
... ratio , and the ratio of the second to the third is equal to the second ratio , and so on , then the first of the set is said to have to the last the ratio compounded of the original ratios . Obs . From these definitions it follows , by ...
Side 206
... on the one are to one another in the same ratio as the corresponding intercepts on the other , Proof . Let the three parallel lines AA ' , 206 [ Book IV . ELEMENTARY GEOMETRY . Let BE, DF be equimultiples of AB, CD...
... on the one are to one another in the same ratio as the corresponding intercepts on the other , Proof . Let the three parallel lines AA ' , 206 [ Book IV . ELEMENTARY GEOMETRY . Let BE, DF be equimultiples of AB, CD...
Side 209
... ratio . THEOREM 3 . A straight line which divides the sides of a triangle pro- portionally is parallel to the base of the triangle . Let AP PB :: AQ : QC ; then will PQ be parallel to BC . For if not , if possible let some other line PQ ...
... ratio . THEOREM 3 . A straight line which divides the sides of a triangle pro- portionally is parallel to the base of the triangle . Let AP PB :: AQ : QC ; then will PQ be parallel to BC . For if not , if possible let some other line PQ ...
Side 211
... angle or sector A'O'N ; and therefore as AB : A'B ' :: angle or sector AOB : angle or sector A'O'B ' . BOOK V. PROPORTION . INTRODUCTION . [ For the use 14-2 SECT . II . ] 211 OF RATIO AND PROPORTION . For let AM be an arc = m. AB...
... angle or sector A'O'N ; and therefore as AB : A'B ' :: angle or sector AOB : angle or sector A'O'B ' . BOOK V. PROPORTION . INTRODUCTION . [ For the use 14-2 SECT . II . ] 211 OF RATIO AND PROPORTION . For let AM be an arc = m. AB...
Side 215
... ratio of A to B is denoted thus , A : B , and A is called the antecedent , B the consequent . The complete ... ratio A : B is equal to the ratio PQ , i.e. either ( 1 ) When A is the same multiple , part , or multiple of a part of B as P ...
... ratio of A to B is denoted thus , A : B , and A is called the antecedent , B the consequent . The complete ... ratio A : B is equal to the ratio PQ , i.e. either ( 1 ) When A is the same multiple , part , or multiple of a part of B as P ...
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AB² ABCD alternate angles angle ABC angle APB angle BAC angles are equal angles equal bisector centre chord circumference coincide College Constr construct contrapositive Crown 8vo describe a circle diagonals diameter divided draw Edition equal angles equal circles equiangular Euclid exterior angle fcap Find the locus four right angles Geometry given angle given circle given line given point given rectilineal figure given straight line hypotenuse included angle inscribed intersect isosceles triangle less Let AB Let ABC locus magnitudes meet middle point minor arc opposite angles opposite sides parallel parallelogram perpendicular polygon PROBLEM produced Proof Q. E. D. THEOREM quadrilateral radius rectangle contained reflex angle required to prove rhombus right angles segment semicircle Shew square subtend supplementary supplementary angles tangent THEOREM trapezium triangle ABC triangles are equal unequal
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