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

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Page 134

A straight line is said to be cut in extreme and mean ratio , when the whole is to the greater segment , as the greater segment is to the less . IV . The

A straight line is said to be cut in extreme and mean ratio , when the whole is to 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 ... Page 135

EA HGBC D Triangles and parallelograms of the same

EA HGBC D Triangles and parallelograms of the same

**altitude**are one See N. to another as their bases . Let the triangles ABC , ACD , and the parallelogramot / 10:07 . ( 16 . EC , CF , have the same**altitude**, viz . the perpendicularis ... Page 136

From this it is plain , that triangles and parallelograms that have equal

From this it is plain , that triangles and parallelograms that have equal

**altitudes**are one to another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars from ... Page 202

See N. Solid parallelopipeds upon the same base , and of the same

See N. Solid parallelopipeds upon the same base , and of the same

**altitude**, the insisting straight lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . Page 203

Solid parallelopipeds upon the same base , and of the same See N.

Solid parallelopipeds upon the same base , and of the same See N.

**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 .### 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

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole