The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 127
V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ...
V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ...
Page 128
When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination still by unity , in any ...
When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination still by unity , in any ...
Page 129
This word is used when there are four proportionals , and it is inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second to the fourth : as is shown in ...
This word is used when there are four proportionals , and it is inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second to the fourth : as is shown in ...
Page 130
Convertendo , by conversion ; when there are four proportionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the fourth . Prop . E. Book 5 . XVIII .
Convertendo , by conversion ; when there are four proportionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the fourth . Prop . E. Book 5 . XVIII .
Page 131
first rank , so is the last but two to the last but one of the second rank ; and as the third is to the fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order : and ...
first rank , so is the last but two to the last but one of the second rank ; and as the third is to the fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order : and ...
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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 |