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

### Inni boken

Resultat 1-5 av 41

Side 126

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**multiple**of a less , when the greater is measured by the less , that is , ' when the greater contains the less a certain num- ' ber of times exactly . ' III . " Ratio is a mutual relation of two magnitudes of the same kind to one ... Side 127

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**multiple**of the first be less than that of the second , the**multiple**of the third is also less than that of the fourth ; or , if the**multiple**of the first be equal to that of the second , the**multiple**of the third is also equal to ... Side 131

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**multiple**of a greater magnitude is greater than the same**multiple**of a less . IV . That magnitude , of which a**multiple**is greater than the same**multiple**of another , is greater than that other magnitude . PROP . I. THEOR . If any ... Side 132

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**multiple**soever any one of them is of its part , the same**multiple**shall all the first magnitudes be of all the other ; ' For ' the same demonstration holds in any number of mag- ' nitudes , which was here applied to two . ' Q. E. D. ... Side 133

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**multiple**of C that DH is of F ; that is , AG , the first and fifth together , is the same mul- tiple of C the second , that DH , the third and sixth together , is of F the fourth . If , therefore , the first be & the same**multiple**, & c ...### Andre utgaver - Vis alle

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1838 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 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.

Side 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.

Side 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.

Side 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.

Side 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.

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

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

Side 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.

Side 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.

Side 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.