The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 4
Multilateral figures , or polygons , by more than four straight lines . XXIV . Of three - sided figures , an equilateral triangle is that which has three equal sides XXV . An isosceles triangle is that which has only two sides equal .
Multilateral figures , or polygons , by more than four straight lines . XXIV . Of three - sided figures , an equilateral triangle is that which has three equal sides XXV . An isosceles triangle is that which has only two sides equal .
Page 191
Similar , polygons may be divideil into the same number of similar triangles , having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicute ratio of that which their homologous sides ...
Similar , polygons may be divideil into the same number of similar triangles , having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicute ratio of that which their homologous sides ...
Page 192
6 . polygons ABCDE , FGHKL may be divided into the same number of similar triangles , whereof each shall have to each the same ratio which the polygons have ; and the polygon ABCDE shall have to the polygon FGHKL the duplicate ratio of ...
6 . polygons ABCDE , FGHKL may be divided into the same number of similar triangles , whereof each shall have to each the same ratio which the polygons have ; and the polygon ABCDE shall have to the polygon FGHKL the duplicate ratio of ...
Page 193
the same ratio which the polygons have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : and the polygon ABCDE shall have to the polygon FGHKL the duplicate ratio of that which the side AB ...
the same ratio which the polygons have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : and the polygon ABCDE shall have to the polygon FGHKL the duplicate ratio of that which the side AB ...
Page 194
5 . fore also the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which AB has to the homologous side FG . Wherefore similar polygons , & c . Q. E. D. Cor . 1 .-- In like mannerit may be proved that similar four ...
5 . fore also the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which AB has to the homologous side FG . Wherefore similar polygons , & c . Q. E. D. Cor . 1 .-- In like mannerit may be proved that similar four ...
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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 |