## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |

### Dentro del libro

Resultados 1-5 de 43

Página 8

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**shewn**that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a ... Página 11

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**shewn**that AB is not less than AC ; that is , AB is equal to AC . B COR . - Hence every equiangular triangle is also equilateral . PROPOSITION VII . THEOREM . Upon the same base , and on the same side of it , there cannot be two ... Página 12

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**shewn**to be greater than the angle BCD ; therefore BC is not equal to BD . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD , to E , F ; then , because AC is equal to AD in the triangle ACD , the ... Página 15

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**shewn**as follows : The angle DBA is greater than a right angle by the angle EBA , and the angle ABC is less than a right angle by the same angle EBA ; therefore their sum is two right angles . COR . - Hence if one of a pair of ... Página 18

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**shewn**that it is not equal to AB ; therefore AC is greater than AB . PROPOSITION XX . THEOREM . Any two sides of a triangle are together greater than the third side . Given a triangle ABC ; to prove that together are greater than the ...### Otras ediciones - Ver todas

Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Sin vista previa disponible - 2023 |

Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Sin vista previa disponible - 2018 |

### Términos y frases comunes

ABCD adjacent angles angle ABC angle ACB angle BAC apothem base BC BC is equal bisected centre Chambers's chord circle ABC circumference Const cosec cosine described diameter divided double draw equal angles equal to twice equiangular equilateral equilateral polygon equimultiples exterior angle fore given line given point given straight line gnomon greater hence hypotenuse inscribed isosceles triangle less line drawn multiple number of sides opposite angle parallel parallelogram perimeter perpendicular polygon produced proportional PROPOSITION prove radius ratio rectangle contained rectilineal figure regular polygon remaining angle right angles right-angled triangle segment semiperimeter shewn similar sine square on AC straight line AC tangent THEOREM third touches the circle triangle ABC triangle DEF twice the rectangle vertical angle wherefore

### Pasajes populares

Página 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Página 52 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.

Página 51 - 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 53 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC...

Página 3 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Página 29 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Página 117 - And the same thing is to be understood when it is more briefly expressed by saying, a has to d the ratio compounded of the ratios of e to f, g to h, and k to l. In like manner, the same things being supposed, if m has to n the same ratio which a has to d ', then, for shortness...

Página 13 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

Página 159 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.

Página 60 - CB, BA, by twice the rectangle CB, BD. Secondly, Let AD fall without the triangle ABC. Then, because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i.