The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 58
... bisected , and produced to any point , the rectangle contained by the whole line thus pro- duced , and the part of it produced , together with the square on half the line bisected , is equal to the square on the straight line which is ...
... bisected , and produced to any point , the rectangle contained by the whole line thus pro- duced , and the part of it produced , together with the square on half the line bisected , is equal to the square on the straight line which is ...
Side 64
... bisected and of the square on the line made up of the half and the part produced . Let the straight line AB be bisected at C , and pro- duced to D : the squares on AD , DB shall be together double of the squares on AC , CD . From the ...
... bisected and of the square on the line made up of the half and the part produced . Let the straight line AB be bisected at C , and pro- duced to D : the squares on AD , DB shall be together double of the squares on AC , CD . From the ...
Side 102
... bisect it . Join AB ; bisect it at C ; [ I. 10 . from the point C draw CD at right angles to AB meeting the arc at D. [ I. 11 . The arc ADB shall be bisected at the point D. Join AD , DB . Then , because AC is equal to CB ...
... bisect it . Join AB ; bisect it at C ; [ I. 10 . from the point C draw CD at right angles to AB meeting the arc at D. [ I. 11 . The arc ADB shall be bisected at the point D. Join AD , DB . Then , because AC is equal to CB ...
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Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles 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 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