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

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Page 167

III . 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

III . 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 167 ... Page 168

The

The

**altitude**of any figure is the straight line drawn from its vertex perpendicular to the base . > PROP . I. THEOR . Triangles and parallelograms of the same**altitude**are one to another as their bases . Page 169

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 170

... having the same

... having the same

**altitude**, viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to the triangle ADE , so is CE to EA : therefore , as BD to DA ... Page 254

Solid parallelopipeds upon the same base , and of the same

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 .### 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

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole