Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
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Página 113
For the same reason the multiples of nB and nD by q , are qnB , qn D , Since , therefore , A : B :: C : D ... If one magnitude be the same multiple of another , which a magnitude taken from the first is of a mugnitude taken from the ...
For the same reason the multiples of nB and nD by q , are qnB , qn D , Since , therefore , A : B :: C : D ... If one magnitude be the same multiple of another , which a magnitude taken from the first is of a mugnitude taken from the ...
Página 114
1 from a multiple of a magnitude by any number a multiple of the same magnitude by a less number be taken away , the remainder will be the same multiple of that magnitude that the difference of the numbers is of unity .
1 from a multiple of a magnitude by any number a multiple of the same magnitude by a less number be taken away , the remainder will be the same multiple of that magnitude that the difference of the numbers is of unity .
Página 115
Next , Let ' C be the same part of A that D is of B ; then A is the , same multiple of C that B is of D , and therefore , as has been demonstrated , A : C :: B : D , and inversely ( A. 5. ) C : A :: D : B . Therefore , & c .
Next , Let ' C be the same part of A that D is of B ; then A is the , same multiple of C that B is of D , and therefore , as has been demonstrated , A : C :: B : D , and inversely ( A. 5. ) C : A :: D : B . Therefore , & c .
Página 116
A + B has to C a greater ratio than A has to C ; and C has a greater C ratio to A than it has to A + B . Let m be such a number that mĄ and mB are each of them greater than C ; and let nC be the least multiple of C that exceeds ma + mB ...
A + B has to C a greater ratio than A has to C ; and C has a greater C ratio to A than it has to A + B . Let m be such a number that mĄ and mB are each of them greater than C ; and let nC be the least multiple of C that exceeds ma + mB ...
Página 118
... has to the fourth , the first will have to the second the same ratio which the third has to the fourth . If A + B : B :: C - 4D : D , then by division A : B :: C : D . : > Take mA and nB any multiples of A and B 118 ELEMENTS.
... has to the fourth , the first will have to the second the same ratio which the third has to the fourth . If A + B : B :: C - 4D : D , then by division A : B :: C : D . : > Take mA and nB any multiples of A and B 118 ELEMENTS.
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Información bibliográfica
| Título | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
| Autor | John Playfair |
| Editor | E. Duyckinck, and George Long, 1824 |
| Procedencia del original | Universidad de Indiana |
| Digitalizado | 15 Ene. 2009 |
| Largo | 333 páginas |
| Exportar cita | BiBTeX EndNote RefMan |