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 3
Division , or the ratio of one quantity to another , is usually denoted by placing one of the two quantities over the other , in the form of a fraction : A thus , ö signifies the ratio or quotient arising from the division of the B ...
Division , or the ratio of one quantity to another , is usually denoted by placing one of the two quantities over the other , in the form of a fraction : A thus , ö signifies the ratio or quotient arising from the division of the B ...
Página 100
... when the greater contains the less a certain number of times exactly . 3. Ratio is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . 4. Magnitudes are said to be of the same kind.
... when the greater contains the less a certain number of times exactly . 3. Ratio is a mutual relation of two magnitudes , of the same kind , to one another , in respect of quantity . 4. Magnitudes are said to be of the same kind.
Página 101
Magnitudes are said to be of the same kind , when the less can be multiplied so as to exceed the greater ; and it is only such magnitudes that are said to have a ratio to one another . 5. If there be four magnitudes , and if any ...
Magnitudes are said to be of the same kind , when the less can be multiplied so as to exceed the greater ; and it is only such magnitudes that are said to have a ratio to one another . 5. If there be four magnitudes , and if any ...
Página 102
In like manner , the same things being supposed , if M'has to N the same ratio which A has to D , then , for shortness ' sake , M is said to have to N a ratio compounded of the same ratios which compound the ratio of A to D ; that is ...
In like manner , the same things being supposed , if M'has to N the same ratio which A has to D , then , for shortness ' sake , M is said to have to N a ratio compounded of the same ratios which compound the ratio of A to D ; that is ...
Página 105
If the first of four magnitudes has the same ratio to the second which the third has to the fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the ...
If the first of four magnitudes has the same ratio to the second which the third has to the fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the ...
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Términos y frases comunes
ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch 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 | W. E. Dean, 1836 |
| Largo | 311 páginas |
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