A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página 18
If equals be taken from equals the 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 ...
If equals be taken from equals the 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 ...
Página 20
therefore the 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 ...
therefore the 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 ...
Página 24
[ I. 4. ] And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hyp . ] the remainder BF is equal to the remainder CG . [ Ax . 3. ] And FC was proved to be equal to GB ; therefore the ...
[ I. 4. ] And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hyp . ] the remainder BF is equal to the remainder CG . [ Ax . 3. ] And FC was proved to be equal to GB ; therefore the ...
Página 63
... then , because ABCD is a parallelogram AD is equal to BC ; [ I. 34. ] for the same reason EF is equal to BC ; therefore AD is equal to EF ; [ Ax . 1. ] therefore the whole , or the remainder , AE is equal to the whole ...
... then , because ABCD is a parallelogram AD is equal to BC ; [ I. 34. ] for the same reason EF is equal to BC ; therefore AD is equal to EF ; [ Ax . 1. ] therefore the whole , or the remainder , AE is equal to the whole ...
Página 64
trapezium take the triangle EAB , and the remainders are equal ; [ Ax . 3. ] ... Q.E.D. In the phrase the whole or remainder , which occurs in the demonstration , the whole refers to the left - hand figure , where AE is the sum of AD and ...
trapezium take the triangle EAB , and the remainders are equal ; [ Ax . 3. ] ... Q.E.D. In the phrase the whole or remainder , which occurs in the demonstration , the whole refers to the left - hand figure , where AE is the sum of AD and ...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
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
ABCD AC is equal alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal apply axioms base BC bisect BOOK called centre circle coincide common Const construction definitions demonstration describe diagonals diameter difference divided double draw equal sides equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater Hence isosceles triangle join length less Let ABC meet method namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained rectilineal figure remainder result right angles side BC sides square on AC Take THEOREM things triangle ABC true truths twice the rectangle unequal units whole
Información bibliográfica
| Título | A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
| Autor | Euclides |
| Editor | Charles MANSFORD |
| Publicado | 1874 |
| Procedencia del original | Biblioteca Británica |
| Digitalizado | 27 Nov. 2020 |
| Exportar cita | BiBTeX EndNote RefMan |