A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 18
... remainders are equal . 4. If equals be added to unequals the wholes are unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same are equal to one another . 7. Things which are ...
... remainders are equal . 4. If equals be added to unequals the wholes are unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same are equal to one another . 7. Things which are ...
Página 20
... remainder AL is equal to the remainder BG . [ Ax . 3. ] But it has been shown that BC is equal to BG ; therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another . [ Ax . 1 ...
... remainder AL is equal to the remainder BG . [ Ax . 3. ] But it has been shown that BC is equal to BG ; therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another . [ Ax . 1 ...
Página 24
... remainder BF is equal to the remainder CG . [ Ax . 3. ] And FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was proved equal to the angle CGB ...
... remainder BF is equal to the remainder CG . [ Ax . 3. ] And FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was proved equal to the angle CGB ...
Página 63
... remainder , DF . [ Ax . 2 , 3. ] And AB is equal to DC ; [ I. 34. ] there- fore the two EA , AB are equal to the two ... remainders are BOOK I. 35 . 63.
... remainder , DF . [ Ax . 2 , 3. ] And AB is equal to DC ; [ I. 34. ] there- fore the two EA , AB are equal to the two ... remainders are BOOK I. 35 . 63.
Página 64
Euclides Charles Mansford. trapezium take the triangle EAB , and the remainders are equal ; [ Ax . 3. ] that is , the ... remainder to the right - hand figure , where AE is the difference of AD and DE . At this point we enter upon the ...
Euclides Charles Mansford. trapezium take the triangle EAB , and the remainders are equal ; [ Ax . 3. ] that is , the ... remainder to the right - hand figure , where AE is the difference of AD and DE . At this point we enter upon the ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join less Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal