## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 4

Multilateral figures , or

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 ,

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 .

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

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

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 ...### What people are saying - Write a review

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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