The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 4
... 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 . XXVI . A scalene triangle ...
... 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 . XXVI . A scalene triangle ...
Page 191
... polygons may be divided 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 dupli- cute ratio of that which their homologous sides have . Let ...
... polygons may be divided 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 dupli- cute ratio of that which their homologous sides have . Let ...
Page 192
... polygons have ; and the polygon ABCDE shall have to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon * 1 Def . FGHKL ...
... polygons have ; and the polygon ABCDE shall have to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon * 1 Def . FGHKL ...
Page 193
... 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 has to the homologous side ...
... 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 has to the homologous side ...
Page 194
... 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 manner it may be proved that similar four - sided figures , or of ...
... 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 manner it may be proved that similar four - sided figures , or of ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole