## The Elements of Euclid: Viz. the First Six Books, with the Eleventh and Twelfth. In which the Corrections of Dr. Simson are Generally Adopted, But the Errors Overlooked by Him are Corrected, and the Obscurities of His and Other Editions Explained. Also Some of Euclid's Demonstrations are Restored, Others Made Shorter and More General, and Several Useful Propositions are Added. Together with Elements of Plane and Spherical Trigonometry, and a Treatise on Practical Geometry |

### Inni boken

Resultat 1-5 av 10

Side 110

Magnitudes which have the same ratio , are called

four magnitudes are

to the second as the third to the fourth . VII . If fome multiple of the first contain the

...

Magnitudes which have the same ratio , are called

**Proportionals**. N. B. Whenfour magnitudes are

**proportionals**, it is usually expressed by saying , the first isto the second as the third to the fourth . VII . If fome multiple of the first contain the

...

Side 123

F four magnitudes of the same kind be propor , tionals , they shall also be

when taken ...

F four magnitudes of the same kind be propor , tionals , they shall also be

**proportionals**when taken alternately . Let the four magnitudes A , B , CD , EF be**proportionals**, viz . as A to B , so CD to EF : They shall also be**proportionals**when taken ...

Side 125

BOOK V. 1 IF F magnitudes , taken separately , be

be

as CF to FD ; they shall also be

...

BOOK V. 1 IF F magnitudes , taken separately , be

**proportionals**, they shall alsobe

**proportionals**when taken joint . y ; that is , by composition . Let AE be to EB ,as CF to FD ; they shall also be

**proportionals**when taken jointly ; that is , as AB to...

Side 149

XVI . THEOR . I to F four straight lines be

contained by the means : And if the rectangle contained by the extremes be

equal to the rectangle contained by the means , the four straight lines are

XVI . THEOR . I to F four straight lines be

**proportionals**, the rectrectanglecontained by the means : And if the rectangle contained by the extremes be

equal to the rectangle contained by the means , the four straight lines are

**proportionals**. Side 150

Book VI . gram BG is equal to the parallelogram DH ; and they are equiangular :

But the fides about the equal angles of equal C 14.6 . parallelograms are

reciprocally

equal ...

Book VI . gram BG is equal to the parallelogram DH ; and they are equiangular :

But the fides about the equal angles of equal C 14.6 . parallelograms are

reciprocally

**proportional**C : Wherefore , as AB to CD , so is CH to AG ; and CH isequal ...

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### Vanlige uttrykk og setninger

ABC is equal ABCD alſo altitude angle ABC angle BAC arch baſe becauſe biſect Book caſe centre circle circumference common contained cylinder definition demonſtrated deſcribed diameter difference diſtance divided double draw drawn equal equal angles equiangular equimultiples fall fame fides figure firſt folid fore four fourth greater half inches join leſs Let ABC magnitudes mean meaſure meet oppoſite parallel parallelogram parallelopiped paſs perpendicular plane priſm PROB produced PROP proportionals propoſition proved radius rectangle rectangle contained rectilineal remaining right angles ſame ſame multiple ſame reaſon ſecond ſegment ſhall ſides ſimilar ſolid ſquare ſtraight line ſum taken tangent THEOR theſe third touches triangle triangle ABC twice uſe Wherefore whole

### Populære avsnitt

Side 30 - 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.

Side 142 - 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 13 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 30 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

Side 72 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...

Side 57 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...

Side 145 - 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.

Side 48 - 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 35 - F, which is the common vertex of the triangles ; that is, together with four right angles. 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 10 - 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.