The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 130
Exæquali ( sc . distantiâ ) , or ex æquo , from equality of distance : when there is any number of magnitudes more than two , and as many others , such that they are proportionals when taken two and two of each rank , and it is inferred ...
Exæquali ( sc . distantiâ ) , or ex æquo , from equality of distance : when there is any number of magnitudes more than two , and as many others , such that they are proportionals when taken two and two of each rank , and it is inferred ...
Page 133
If the first be the sume multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples ; these shall be equimultiples , the one of the second , and the other of the fourth .
If the first be the sume multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples ; these shall be equimultiples , the one of the second , and the other of the fourth .
Page 134
... which the equimultiple of the third has to that of the fourthi ' Let A the first have to B the second the same ratio which the third C has to the fourth D ; and * 3.5 of A and C let there be taken 134 EUCLID'S ELEMENTS .
... which the equimultiple of the third has to that of the fourthi ' Let A the first have to B the second the same ratio which the third C has to the fourth D ; and * 3.5 of A and C let there be taken 134 EUCLID'S ELEMENTS .
Page 135
3.5 of A and C let there be taken any equimultiples whatever E , F ; and of B and D any equimultiples whatever G , H : then E shall have the same ratio to G , which F has to H. Take of E and F any equimultiples whatever K , L , and of G ...
3.5 of A and C let there be taken any equimultiples whatever E , F ; and of B and D any equimultiples whatever G , H : then E shall have the same ratio to G , which F has to H. Take of E and F any equimultiples whatever K , L , and of G ...
Page 136
K - is the same multiple of A , that L is of C : and because t A is to B , as C is to D , and of A and C certain equimultiples have been taken , viz . K and L ; and of B and D certain equimultiples G , H ; therefore , if K be greater ...
K - is the same multiple of A , that L is of C : and because t A is to B , as C is to D , and of A and C certain equimultiples have been taken , viz . K and L ; and of B and D certain equimultiples G , H ; therefore , if K be greater ...
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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2013 |
Common terms and phrases
altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole
Bibliographic information
| Title | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Author | Euclid |
| Editors | Robert Simson, Samuel Maynard |
| Translated by | Robert Simson |
| Publisher | Longman, Orme, Brown, Green, and Longmans, 1838 |
| Original from | University of Iowa |
| Digitized | 13 Jul 2015 |
| Length | 328 pages |
| Export Citation | BiBTeX EndNote RefMan |