## 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 8

Side 136

See N. T TRIANGLES and parallelograms of the same

as their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF

have the same

Then ...

See N. T TRIANGLES and parallelograms of the same

**altitude**are one to anotheras their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF

have the same

**altitude**, viz . the perpendicular drawn from the point A to BD :Then ...

Side 198

SOM OLID parallelopipeds upon the fame base , and of the same

insisting straight lines * of which are not terminated in the same straight lines , are

equal to one another . Let the parallelopipeds CM , CN be upon the same base ...

SOM OLID parallelopipeds upon the fame base , and of the same

**altitude**, theinsisting straight lines * of which are not terminated in the same straight lines , are

equal to one another . Let the parallelopipeds CM , CN be upon the same base ...

Side 201

In like manner , it Book XI . may be proved , that the folid YF is a parallelopiped :

But , from what has been demonstrated , the solid EQ is equal to the solid FY ,

because they are upon equal bases MK , PS , and of the same

...

In like manner , it Book XI . may be proved , that the folid YF is a parallelopiped :

But , from what has been demonstrated , the solid EQ is equal to the solid FY ,

because they are upon equal bases MK , PS , and of the same

**altitude**, and have...

Side 204

Book XI . so d is the solid AB , to the folid GL , because they are of the mfame

GL is to the folid CD , as & the base GH is to the base GK ; that is , as the straight

...

Book XI . so d is the solid AB , to the folid GL , because they are of the mfame

**altitude**; therefore the folid AB is to the folid GL , as a to d 32. 11. c : and the solidGL is to the folid CD , as & the base GH is to the base GK ; that is , as the straight

...

Side 205

CD : make OQ equal to the

OP d : Therefore MP is to PT , as MO to d 31. 1 . OQ ; that is , as the

to the

CD : make OQ equal to the

**altitude**of AB ; and join OP , and draw QT parallel toOP d : Therefore MP is to PT , as MO to d 31. 1 . OQ ; that is , as the

**altitude**of CDto the

**altitude**AB . Draw € 2.6 . TV parallel to PC 4 : and let the plane QTV cut ...### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

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### 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.