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Page 134
... magnitudes of the same kind to one another in respect of quantity . 4. Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . 5. The first of four magnitudes is said to have the ...
... magnitudes of the same kind to one another in respect of quantity . 4. Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . 5. The first of four magnitudes is said to have the ...
Page 138
... magnitudes AB , CD_be_equimul- tiples of as many others E , F , each of each : whatever mul- tiple AB of E , the ... magnitudes as there are in AB equal to E , so many are there in CD equal to F. Divide AB into the magnitudes AG , GB ...
... magnitudes AB , CD_be_equimul- tiples of as many others E , F , each of each : whatever mul- tiple AB of E , the ... magnitudes as there are in AB equal to E , so many are there in CD equal to F. Divide AB into the magnitudes AG , GB ...
Page 157
... Magnitudes have the same ratio to one another that their equimultiples have . Let AB be the same multiple of C that ... magnitudes as there are in AB equal to C , so many are there in DE equal to F. Divide AB into the magnitudes AG , GH ...
... Magnitudes have the same ratio to one another that their equimultiples have . Let AB be the same multiple of C that ... magnitudes as there are in AB equal to C , so many are there in DE equal to F. Divide AB into the magnitudes AG , GH ...
Common terms and phrases
ABCD AC is equal angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary Definition 15 demonstration 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 shown sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM touches the circle triangle ABC triangle DEF twice the rectangle Wherefore whole angle