The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 101
... when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , See N. when any equimultiples whatsoever of the first and.
... when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , See N. when any equimultiples whatsoever of the first and.
Page 102
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
Page 105
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . II . Those magnitudes , of which the same or equal magni- tudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is ...
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . II . Those magnitudes , of which the same or equal magni- tudes are equimultiples , are equal to one another . III . A multiple of a greater magnitude is ...
Page 106
... equal to E and F together : therefore , whatso- ever multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes , how many soever , be equimultiples of as many , each of each ...
... equal to E and F together : therefore , whatso- ever multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes , how many soever , be equimultiples of as many , each of each ...
Page 107
... equimultiples ; these shall be equimulti- ples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let equimultiples EF , GH ...
... equimultiples ; these shall be equimulti- ples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let equimultiples EF , GH ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore