## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

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**ratio**to the se- cond and fourth and in like manner , the first and the third have the same**ratio**to any ...**AE**taken from the first , is of CF taken from the other ; the remainder EB shall be the same multiple of the remainder FD , that the ... Page 131

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**ratio**than it has to AB , for , hav- ing made the same construction , it may be shown , inlikeman- ner , that Lis greater**A E**c ! F Fig . 3 . A B L KH D L K D than FG , but that it is not greater than EG : and L is a multiple of D ; and ... Page 138

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**ratio**which two others have to one of these , the remaining one of the first two shall have to the other the same ...**AE**to EB , so CF to FD . Take of**AE**, EB , CF , FD , any equimultiples whatever GH , HK , LM , MN ; and again , of EB ... Page 142

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**AE**, as DC to CF ; and because , if magnitudes , taken jointly , be ...**ratio**; if the first be greater than the third , the fourth shall be greater ...**ratio**, viz . as A is to B , See Note . so is D to**E**; and as B to 142 BOOK V. THE ... Page 175

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**AE**, as GF to FL ( 1. def . 6. ) ; wherefore because the triangles ABE , FGL , have an angle in one**equal**to an ...**ratio**which the polygons have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : ...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore