The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 138
... tiples of as many others E , F , each of each : whatever multiple AB is of E , the same multiple shall AB and CD together , be of E and F together . For , because AB is the same multiple of E , that CD is of F , as many magnitudes as ...
... tiples of as many others E , F , each of each : whatever multiple AB is of E , the same multiple shall AB and CD together , be of E and F together . For , because AB is the same multiple of E , that CD is of F , as many magnitudes as ...
Página 160
... tiples of AB and CD , and FX and MP are equimultiples of EB and FD , therefore if GA be greater than HX , LNis greater than MP ; and if equal , equal ; and if less , less . [ V. Def . 5 . But if GH be greater than KX , then , by adding ...
... tiples of AB and CD , and FX and MP are equimultiples of EB and FD , therefore if GA be greater than HX , LNis greater than MP ; and if equal , equal ; and if less , less . [ V. Def . 5 . But if GH be greater than KX , then , by adding ...
Página 168
... tiples whatever K and L ; and of C and F any equimul- tiples whatever M and N. Then , because A is to B as D is to E ; [ Hypothesis . and that G and H are equi- multiples of A and D , and K and L cquimultiples of B and E ...
... tiples whatever K and L ; and of C and F any equimul- tiples whatever M and N. Then , because A is to B as D is to E ; [ Hypothesis . and that G and H are equi- multiples of A and D , and K and L cquimultiples of B and E ...
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Términos y frases comunes
ABCD adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC BC is equal bisected centre circle ABC circumference Constr Construction Definition 15 demonstration diameter double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given straight line gnomon greater ratio greater than F Hypothesis less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shewn sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM tiples touches the circle triangle ABC triangle DEF twice the rectangle Wherefore