## 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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**given**of com- pound**ratio**, and giving an absurd one in place of it in the 5th Definition of the 6th Book , which ...**given**, is put in its pro- per place among the Definitions of the 5th Book , by which the doctrine of compound**ratios**... Page 173

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**given**straight line simi- lar to one**given**, and so on . Which was to be done . PROP . XIX . THEOR . SIMILAR triangles are to one another in the duplicate**ratio**of their homologous sides . Let ABC , DEF be similar triangles , having the ... Page 186

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**given**rectilineal C , exceeding by the parallelogram PO , which is similar to D , because PO is similar to EL ( 24. 6. ) Which was to be done . PROP . XXX . PROB . To cut a**given**straight line in extreme and mean**ratio**. Let AB be the**given**... Page 187

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**ratio**in E ( 3. def . 6. ) . Which was to be done . Otherwise . C F Let AB be the**given**straight line ; it is required to cut it in extreme and mean**ratio**. Divide AB in the point C , so that the rectangle contained by AB , BC be equal ... Page 299

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**give**the reason why two sides of a triangle are greater than the third : but the ...**ratio**which is less than that of two to one , as Pappus Alexandrinus has ...**given**, viz . that any two of the straight lines DF , FG , GH must be great ...### 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