The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 82
Euclid Isaac Todhunter. PROPOSITION 9. THEOREM . If a point be taken within a circle , from which there fall more than two equal straight lines to the circum- ference , that point is the centre of the circle . Let the point D be taken ...
Euclid Isaac Todhunter. PROPOSITION 9. THEOREM . If a point be taken within a circle , from which there fall more than two equal straight lines to the circum- ference , that point is the centre of the circle . Let the point D be taken ...
Página 164
... taken from the first is to a magnitude taken from the other , the remainder shall be to the remainder as the whole is to the whole . Let the whole AB be to the whole CD as AE , a mag- nitude taken from AB , is to CF , a magnitude taken ...
... taken from the first is to a magnitude taken from the other , the remainder shall be to the remainder as the whole is to the whole . Let the whole AB be to the whole CD as AE , a mag- nitude taken from AB , is to CF , a magnitude taken ...
Página 244
... taken more than its half , and from the remainder more than its half , and so on , there shall at length re- main a magnitude less than the smaller of the proposed magnitudes . Let AB and C be two unequal magnitudes , of which AB is the ...
... taken more than its half , and from the remainder more than its half , and so on , there shall at length re- main a magnitude less than the smaller of the proposed magnitudes . Let AB and C be two unequal magnitudes , of which AB is the ...
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AB is equal 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