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 59
If a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line , and of the square of the line between the points of section .
If a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line , and of the square of the line between the points of section .
Página 60
... and the square of the part of it produced , are together double of the square of half the line bisected , and of ... AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD .
... and the square of the part of it produced , are together double of the square of half the line bisected , and of ... AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD .
Página 64
If one side of a triangle be bisected , the sum of the squares of the other two sides is double of the square of half the side bisected , and of the square of the line drawn from the point of bisection to the opposite angle of the ...
If one side of a triangle be bisected , the sum of the squares of the other two sides is double of the square of half the side bisected , and of the square of the line drawn from the point of bisection to the opposite angle of the ...
Página 76
it ; Where- Α . E fore AF is equal to FB , and AB double of AF . For the same reason , CD is double of CG : But AB is equal to CD ; E therefore AF is equal to CG : And be . cause AE is equal to EC , the square of AE is equal to the ...
it ; Where- Α . E fore AF is equal to FB , and AB double of AF . For the same reason , CD is double of CG : But AB is equal to CD ; E therefore AF is equal to CG : And be . cause AE is equal to EC , the square of AE is equal to the ...
Página 77
than EK : But , as was demonstrated in the preceding , BC is double of BH and FG double of FK , and the squares of EH , HB are equal to the squares of EK , KF , of which the square of EH is less than the square of EK , because EH is ...
than EK : But , as was demonstrated in the preceding , BC is double of BH and FG double of FK , and the squares of EH , HB are equal to the squares of EK , KF , of which the square of EH is less than the square of EK , because EH is ...
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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 |