The text of Euclid's geometry, book 1, uniformly and systematically arranged by J.D. Paul1884 |
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... added in italics , a few other such facts , the consideration of which will afford useful mental exercise . With the hope of encouraging the student to apply , when practicable , superposition in the demonstration of theorems , some ...
... added in italics , a few other such facts , the consideration of which will afford useful mental exercise . With the hope of encouraging the student to apply , when practicable , superposition in the demonstration of theorems , some ...
Página 10
... added to equals the wholes are equal . If equals be added to the same magnitude the wholes are equal . If the same magnitude be taken from equals , the remainders are equal . If equals be taken from the same magnitude the remainders are ...
... added to equals the wholes are equal . If equals be added to the same magnitude the wholes are equal . If the same magnitude be taken from equals , the remainders are equal . If equals be taken from the same magnitude the remainders are ...
Página 12
... added to each , the first whole is greater than the second whole . ( x ) Any one of two unlimited straight lines may be assumed to be greater than a given part of the other , or any other finite straight line . ( y ) The straight line ...
... added to each , the first whole is greater than the second whole . ( x ) Any one of two unlimited straight lines may be assumed to be greater than a given part of the other , or any other finite straight line . ( y ) The straight line ...
Página 16
... added to unequals the wholes are unequal ; the absurdity of this can be easily shown thus : — B E Let AB and DE be two equal straight lines , and let AB be divided into two unequal parts at the point C , so that AC is greater than CB ...
... added to unequals the wholes are unequal ; the absurdity of this can be easily shown thus : — B E Let AB and DE be two equal straight lines , and let AB be divided into two unequal parts at the point C , so that AC is greater than CB ...
Página 70
... added to equals , the wholes are equal . III . If equals be taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal ...
... added to equals , the wholes are equal . III . If equals be taken from equals , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal ...
Términos y frases comunes
2nd Edition 4th Edition AB is equal ABC and DEF ABC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle CAB angle contained angle DEF angle EDF angle equal angle GHD angles are equal angles CBA Axiom 9 base BC BDC is greater bisector bisects centre circle coincide Constr Crown 8vo describe diagonal equal sides equal to BD equal to EF equilateral triangle Euclid exterior angle F. A. Paley Fcap finite straight line Geometry given point given straight line isosceles triangle Join Latin magnitude are equal opposite sides parallel to BC parallelogram parallelogram ABCD plane figure Post 8vo Postulate produced Q. E. D. PROPOSITION quadrilateral rectilineal angle REQUIRED TO PROVE rhombus right angles sides equal square on AC straight line drawn THEOREM triangle ABC triangle DEF triangles are equal vertex Нур
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Página 72 - LET it be granted that a straight line may be drawn from any one point to any other point.
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