## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth ... Also the Book of Euclid's Data, in Like Manner Corrected |

### Inni boken

Side 118

'the

the

equimul- - ; : tiples whatever E, F, and of B. and Dany

G, ...

'the

**equimultiple**' of the first shall have the same ratio to that of 'the second, whichthe

**equimultiple**of the third “ has to ... and of A and C let there be taken anyequimul- - ; : tiples whatever E, F, and of B. and Dany

**equimultiples**what- | - everG, ...

Side 119

119 multiples whatever of the first and third have the same ra- Book V. tio to the

second and fourth : And in like manner, the first S^^* and the third have the same

ratio to any

119 multiples whatever of the first and third have the same ra- Book V. tio to the

second and fourth : And in like manner, the first S^^* and the third have the same

ratio to any

**equimultiples**whatever of the second and fourth. o Let A the first, ... Side 127

Let A have to C a greater ratio than B has to C.; A is greater than B: For, because

A has a greater ratio to C, than B has to C, there are” some

- 7 Def. 5. B, and some multiple of C such, that the multiple of A is greater than ...

Let A have to C a greater ratio than B has to C.; A is greater than B: For, because

A has a greater ratio to C, than B has to C, there are” some

**equimultiples**of A and- 7 Def. 5. B, and some multiple of C such, that the multiple of A is greater than ...

Side 134

Book V. * 3 Ax. 5. w are

which is a multiple of the same BE, NP likewise the multiple of DF, shall be

greater than MN, ...

Book V. * 3 Ax. 5. w are

**equimultiples**of BE, DF; and that KH, NM are**equimultiples**likewise of BE, DF, if KO, the multiple of BE, be greater than KH,which is a multiple of the same BE, NP likewise the multiple of DF, shall be

greater than MN, ...

Side 140

And because H as B is to C, so is D to E, and that H, K, are

, and L, M of C, E; as H is to L, so is e K to M ; And |. it has been shown that G is to

H, as M to N: Then because there are three magnitudes G, H, L, and other three ...

And because H as B is to C, so is D to E, and that H, K, are

**equimultiples*** of B, D, and L, M of C, E; as H is to L, so is e K to M ; And |. it has been shown that G is to

H, as M to N: Then because there are three magnitudes G, H, L, and other three ...

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### Vanlige uttrykk og setninger

ABC is given ABCD AC is equal altitude angle ABC angle BAC arch base BC bisected Book XI centre circle ABC circumference common logarithm cone cosine cylinder demonstration described diameter drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater Greek text hypothenuse join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular polygon prisms proportionals proposition Q.E.D. PROP radius rectangle CB rectangle contained rectilineal figure right angles segment side BC similar sine solid angle solid parallelopipeds spherical angle spherical triangle square of BC straight line BC tangent THEOR third triangle ABC vertex wherefore

### Populære avsnitt

Side 41 - 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 180 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 166 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides. DH Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14.

Side 2 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.

Side 105 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Side 79 - 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 1 - A straight line is that which lies evenly between its extreme points.

Side 149 - 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 23 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Side 83 - Wherefore from the given circle ABC has been cut off the segment BAC, containing an angle equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the...