## The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendixThomas Tegg, 1841 - 351 páginas |

### Dentro del libro

Resultados 1-5 de 44

Página 167

... other is to the remaining " side of the first . " 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 . * 3. 1 . The

... other is to the remaining " side of the first . " 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 . * 3. 1 . The

**altitude**of any. Página 168

...

...

**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 , or BD produced : then , as the base BC is to the ... Página 169

...

...

**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 perpen- diculars from the vertices of the triangles to the bases , the straight line which ... Página 170

...

...

**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 11. 5. BD to DA , so is CE to ... Página 254

...

...

**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 . Let the parallelopipeds AH , AK be upon the same base AB , and of the same**altitude**...### Otras ediciones - Ver todas

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Sin vista previa disponible - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid Sin vista previa disponible - 2023 |

### Términos y frases comunes

AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole

### Pasajes populares

Página 173 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Página 56 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Página 53 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Página 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Página 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Página 23 - Any two sides of a triangle are together greater than the third side.

Página 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.

Página 103 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.

Página 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Página 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.