## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 19

Side 102

Thus, 3A signifies three times A; mB, m times B, or a

number is intended to multiply two or more magnitudes that follow, it is written

thus, m §§ which signifies the sum of A and B taken m times; m (A–B) is m times ...

Thus, 3A signifies three times A; mB, m times B, or a

**multiple**of B by m. When thenumber is intended to multiply two or more magnitudes that follow, it is written

thus, m §§ which signifies the sum of A and B taken m times; m (A–B) is m times ...

Side 103

... is contained a certain number of times, exactly, in the greater. II. A greater

magnitude is said to be a

less; that is, when the greater contains the less a certain number of times exactly.

III.

... is contained a certain number of times, exactly, in the greater. II. A greater

magnitude is said to be a

**multiple**of a less, when the greater is measured by theless; that is, when the greater contains the less a certain number of times exactly.

III.

Side 104

When of the equimultiples of four magnitudes, taken as in the fifth definition, the

not greater than the

When of the equimultiples of four magnitudes, taken as in the fifth definition, the

**multiple**of the first is greater than that of the second, but the**multiple**of the third isnot greater than the

**multiple**of the fourth; then the first is said to have to the ... Side 106

... are equal to one another. w III. A

the same

than the same

... are equal to one another. w III. A

**multiple**of a greater magnitude is greater thanthe same

**multiple**of a less. - IV. That magnitude of which a**multiple**is greaterthan the same

**multiple**of another, is greater than that other magnitude. / PROP. Side 107

If any number of magnitudes be equimultiples of as many others, each of each,

what

of s all the first of the sum of all the rest. Let any number of magnitudes A, B, and ...

If any number of magnitudes be equimultiples of as many others, each of each,

what

**multiple**soever any one of the first is of its part, the same**multiple**is the sumof s all the first of the sum of all the rest. Let any number of magnitudes A, B, and ...

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclides,John Playfair Uten tilgangsbegrensning - 1826 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1851 |

Elements of Geometry;: Containing the First Six Books of Euclid, with a ... Formerly Chairman Department of Immunology John Playfair Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition pyramid Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore

### Populære avsnitt

Side 125 - 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 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.

Side 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Side 19 - 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 straight line AL has been drawn equal to the given straight line BC.

Side 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.

Side 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.

Side 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.

Side 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.

Side 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.