## 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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Page 118

... ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying ...

... ratio are called proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying ...

**triplicate ratio**of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination ... Page 234

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**triplicate ratio**of their homologous sides . Let AB , CD be similar solid parallelopipeds , and the side AE homologous to the side CF : the solid AB has to the solid CD the**triplicate ratio**of that which AE has to CF. pa- Produce AE ... Page 235

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**triplicate ratio**of that which it has to the second : therefore the solid AB has to the solid KO the**triplicate ratio**of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the pa- rallelogram GK , and the ... Page 264

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**triplicate ratio**of that of their homologous sides . Let the pyramids having the triangles ABC , DEF for their bases , and the points G , H for their vertices , be similar , and si- milarly situated ; the pyramid ABCG has to the pyramid ... Page 265

... triplicate ( 33. 11. ) ratio of that which their homologous sides have therefore the solid BGML has to the solid EHPO the

... triplicate ( 33. 11. ) ratio of that which their homologous sides have therefore the solid BGML has to the solid EHPO the

**triplicate ratio**of that which the side BC has to the homologous side EF : but as the solid BGML is to the solid ...### 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