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

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Resultat 6-10 av 26

Side 143

... but B = B are each equal to and one , and taking away these equals , there

remains theine AC and therefore A : B : : C : D . 1974 PROPOSITION XVIII .

THEOREM . ( EUCLID XVIII . ) . The terms of an analogy are

composition .

... but B = B are each equal to and one , and taking away these equals , there

remains theine AC and therefore A : B : : C : D . 1974 PROPOSITION XVIII .

THEOREM . ( EUCLID XVIII . ) . The terms of an analogy are

**proportional**bycomposition .

Side 144

... same manner it may be demonstrated that if C is greater than A , C A : D - B : :

A : B , or as C : D . PROPOSITION XX . THEOREM . ( EUCLID D . ) The terms of

an análogy are

...

... same manner it may be demonstrated that if C is greater than A , C A : D - B : :

A : B , or as C : D . PROPOSITION XX . THEOREM . ( EUCLID D . ) The terms of

an análogy are

**proportional**by conversion . Given that A : B : : C : D ; to prove that...

Side 148

Euclides James Pryde. PROPOSITION XXVII . THEOREM . If four magnitudes be

other two . Given that A : B : : C : D , and that A is the greatest term ; to prove that

A + ...

Euclides James Pryde. PROPOSITION XXVII . THEOREM . If four magnitudes be

**proportional**, the sum of the greatest and least is greater than the sum of theother two . Given that A : B : : C : D , and that A is the greatest term ; to prove that

A + ...

Side 149

Straight lines are said to be similarly divided when their corresponding segments

are

have that ratio . 3 . Straight lines that meet in the same point are called

convergent ...

Straight lines are said to be similarly divided when their corresponding segments

are

**proportional**2 . A line is said to be cut in a given ratio when its “ segmentshave that ratio . 3 . Straight lines that meet in the same point are called

convergent ...

Side 158

From this it is manifest that the perpendicular drawn from the right angle of a right

- angled triangle to the base , is a mean

the · base ; and also that each of the sides is a mean propor; tional between the ...

From this it is manifest that the perpendicular drawn from the right angle of a right

- angled triangle to the base , is a mean

**proportional**between the segments ofthe · base ; and also that each of the sides is a mean propor; tional between the ...

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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... Euclides Uten tilgangsbegrensning - 1860 |

Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Ingen forhåndsvisning tilgjengelig - 2018 |

Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD alternate angle ABC angle BAC base BC is equal bisected called centre chord circle ABC circumference common Const demonstrated described diameter difference divided double draw equal equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given line given point given straight line greater half hence inscribed join less magnitudes manner meet multiple namely parallel parallelogram pass perpendicular polygon PROBLEM produced proportional PROPOSITION prove radius ratio reason rectangle contained rectilineal figure remaining angle respectively right angles segment shewn sides similar square square on AC straight line Take taken tangent THEOREM third triangle ABC twice the rectangle wherefore whole

### Populære avsnitt

Side 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...

Side 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.

Side 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.

Side 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...

Side 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.

Side 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.

Side 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...

Side 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.

Side 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.

Side 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.