The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 126
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less , that is , ' when the greater contains the less a certain number of times exactly . ' III . “ Ratio a mutual relation of two magnitudes ...
A greater magnitude is said to be a multiple of a less , when the greater is measured by the less , that is , ' when the greater contains the less a certain number of times exactly . ' III . “ Ratio a mutual relation of two magnitudes ...
Page 127
When of the 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 ...
When of the 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 ...
Page 131
A multiple of a greater magnitude is greater than the same multiple of a less . ... If any number of magnitudes be equimultiples of as many , each of each ; what multiple soever any one of them is of its part , the same multiple shall ...
A multiple of a greater magnitude is greater than the same multiple of a less . ... If any number of magnitudes be equimultiples of as many , each of each ; what multiple soever any one of them is of its part , the same multiple shall ...
Page 132
L Because AB is the same multiple of E that CD is of F , as many magnitudes as there are in AB equal to E , so many are there in CD equal to F. Divide AB into magnitudes equal to E , viz . AG , GB ; and G E CD into CH , HD , equal each ...
L Because AB is the same multiple of E that CD is of F , as many magnitudes as there are in AB equal to E , so many are there in CD equal to F. Divide AB into magnitudes equal to E , viz . AG , GB ; and G E CD into CH , HD , equal each ...
Page 133
second , that EH the sixth is of D F the fourth : then shall AG , the A Arst together with the fifth , be EN the same multiple of C the se- B fond , that DH , the third together with the sixth , is of F the fourth .
second , that EH the sixth is of D F the fourth : then shall AG , the A Arst together with the fifth , be EN the same multiple of C the se- B fond , that DH , the third together with the sixth , is of F the fourth .
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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |
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 |