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, 1836 - 311 páginas |
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Página 101
... equimultiples whatsoever be taken of the first and third , and any equimultiples whatsoever of the se- cond and fourth , and if , according as the multiple of the first is greater than the multiple of the second , equal to it , or less ...
... equimultiples whatsoever be taken of the first and third , and any equimultiples whatsoever of the se- cond and fourth , and if , according as the multiple of the first is greater than the multiple of the second , equal to it , or less ...
Página 103
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes of which the same , or equal magnitudes , are equi- multiples , are equal to one another . 3. A multiple of a greater magnitude is ...
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes of which the same , or equal magnitudes , are equi- multiples , are equal to one another . 3. A multiple of a greater magnitude is ...
Página 104
... equimultiple of D , E , and F , it would be shown that A + B + C was the same multiple of D + E + F . 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 ...
... equimultiple of D , E , and F , it would be shown that A + B + C was the same multiple of D + E + F . 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 ...
Página 105
... equimultiples by any number p , and of nB and nD equimultiples by any number q . Then the equimultiples of mA , and mC by p , are equimultiples also of A and C , for they contain A and C as oft as there are units in pm ( 3. 5. ) , and ...
... equimultiples by any number p , and of nB and nD equimultiples by any number q . Then the equimultiples of mA , and mC by p , are equimultiples also of A and C , for they contain A and C as oft as there are units in pm ( 3. 5. ) , and ...
Página 106
... equimultiples of A and C ; nB and nD any equi- multiples of B and D. Then , because A : B :: C : D , if mA be less than nB , mC will be less than nD ( def . 5. 5. ) , that is , if nB be greater than mA , nD will be greater than mC . For ...
... equimultiples of A and C ; nB and nD any equi- multiples of B and D. Then , because A : B :: C : D , if mA be less than nB , mC will be less than nD ( def . 5. 5. ) , that is , if nB be greater than mA , nD will be greater than mC . For ...
Otras ediciones - Ver todas
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
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 |
| Edición | 6 |
| Editor | W.E. Dean, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |