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 TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página 107
... multiple of B by m . " When the number is intended to multiply two or more magnitudes " that follow , it is written thus , m ( A + B ) , which signifies the sum ❝of A and B taken m times ; m ( À - B ) is m times the excess of A " above ...
... multiple of B by m . " When the number is intended to multiply two or more magnitudes " that follow , it is written thus , m ( A + B ) , which signifies the sum ❝of A and B taken m times ; m ( À - B ) is m times the excess of A " above ...
Página 108
... multiple of a less , when the great- er is measured by the less , that is , when the greater contains the less a ... multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is ...
... multiple of a less , when the great- er is measured by the less , that is , when the greater contains the less a ... multiple of the first is greater than the multiple of the second , equal to it , or less , the multiple of the third is ...
Página 109
... multiple of the first is greater than that of the se- cond , but the multiple of the third is not greater than the mul- tiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to ...
... multiple of the first is greater than that of the se- cond , but the multiple of the third is not greater than the mul- tiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to ...
Página 111
... multiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude of which a multiple is greater than the same multi- ple of another , is greater than that ...
... multiples , are equal to one another . III . A multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude of which a multiple is greater than the same multi- ple of another , is greater than that ...
Página 112
... multiple D + E + F . Therefore , & c . Q. E. D. COR . Hence , if m be any number , mD + mE + mF = m ( D + E + F ) . For mD , mE , and mF are multiples of D , E , and F by m , therefore their sum is also a multiple of D + E + F by m ...
... multiple D + E + F . Therefore , & c . Q. E. D. COR . Hence , if m be any number , mD + mE + mF = m ( D + E + F ) . For mD , mE , and mF are multiples of D , E , and F by m , therefore their sum is also a multiple of D + E + F by m ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore