The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 1-5 of 69
Page 126
“ Ratio a mutual relation of two magnitudes “ of the same kind to one another , in respect • of quantity . ” IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other .
“ Ratio a mutual relation of two magnitudes “ of the same kind to one another , in respect • of quantity . ” IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other .
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
X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth ...
X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth ...
Page 129
6 6 : D ; then , for shortness sake , M is said to have to N the ratio compounded of the ratios of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are called homologous to one another , as also the ...
6 6 : D ; then , for shortness sake , M is said to have to N the ratio compounded of the ratios of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are called homologous to one another , as also the ...
Page 134
If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , vis .
If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , vis .
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
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 |