## 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

Results 1-5 of 38

Page 153

... greater segment , as the greater segment is to the less . IV . The

... greater segment , as the greater segment is to the less . IV . The

**altitude**of any figure is the straight line- drawn from its vertex perpendicular to the base . * See Note . U PROP . I. THEOR . TRIANGLES and parallelograms of the. Page 154

...

...

**altitude**are one to another as their bases . * Let the triangles ABC , ACD , and the parallelograms EC , CF , have the same**altitude**, viz . the perpendicular drawn from the point A to BD : then , as the base BC is to the base CD , so ... Page 155

...

...

**altitudes**, are one to another as their bases . Let the figures be placed so as to have their bases in the same ...**altitude**, viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ... Page 227

...

...

**altitude**, the insisting lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the solid parallelopipeds AH , AK be upon the same basc AB , and of the same**altitude**... Page 229

...

...

**altitude**, the insisting straight lines of which are not terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the parallelopipeds CM , CN be upon the same base AB , and of the same ...### 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