## 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 |

### From inside the book

Results 1-5 of 20

Page 108

...

...

**equimultiples**whatsoever be taken of the first and third , and any**equimultiples**whatsoever of the second and fourth , and if , according as the multiple of the first is greater than the multiple of the second , equal to it , or less ... Page 109

...

...

**equimultiples**of four magnitudes , taken as in the fifth definition , the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said ... Page 111

...

...

**EQUIMULTIPLES**of the same , or of equal magnitudes , are equal to one another . II . Those magnitudes of which the same , or equal magnitudes , are**equi- multiples**, are equal to one another . III . A multiple of a greater magnitude is ... Page 112

...

...

**equimultiples**of as many others , D , E , and F , each of each A + B + C is the same mul- tiple of D + E + F , that ...**equimultiple**of D , E , and F , it would be shewn that A + B + C was the same multiple of D + E + F . Therefore ... Page 113

...

...

**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 are ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition 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 MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals 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 parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore