## 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

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Página 135

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**tiples**whatever K , L , and of G , H , any equimultiples whatever M , N : then , because E is the L same multiple of A , that F is of C ; and of E and F have been taken equimultiples K , L ; there- fore K is the same multiple of A ... Página 139

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**tiples*** * whatever of B and D , and G and H any what- * Const . ever of A and C ; therefore , as B is to A , so is ...**tiple**of A , that F is of C ; therefore E is the same multiple of B , that F is of D ; * that is , E and F are ... Página 140

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**tiples**whatever of B , D : therefore A is to B , as C is 5 Def . to D. * , 5 . Next , let A the first be the same part of B the second , that C the third is of D the fourth : A shall be to B , as C is to D. For since A is the same part ... Página 146

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**tiples**whatever of A , E ; and L , N any whatever of * 5 Def . B , F : therefore , as A is to B , so is E to F. * Where- fore , ratios that , & c . Q. E. D. 5 . PROP . XII . THEOR . If any number of magnitudes be proportionals , as one ... Página 150

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**tiples**of C , D , therefore as 15. 5. C is to D , so is G to H ; * B H But when four but it was proved that as C is to D , so is E to F ; 11. 5. therefore , as E is to F , so is G to H. magnitudes are proportionals , if the than the ...### 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.