## The Elements of Euclid |

### From inside the book

Results 1-5 of 38

Page 155

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 Book VI . PROP , I. THEOR See Note . Page 156

TRIANGLES and parallelograms of the same

TRIANGLES and parallelograms of the same

**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 front the point A to BD : then ... Page 157

Erom this it is plain , that triangles and parallelograms that haye equal

Erom this it is plain , that triangles and parallelograms that haye 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 ... Page 229

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 See Note : opposite to the basc , are equal to one another . Book XI . Page 230

Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same

Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same

**altitude**, and let their insisting straight See the lines AF , AG , LM , LN be terminated in the same straight figures line FN , and CD , CE , BH , BK be ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

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