## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 22

Side 4

Also the

explicit , and a more general Demonstration is given , instead of that which was in

the

Also the

**Note**on the 29th Proposition , Book 1st , is altered , and made moreexplicit , and a more general Demonstration is given , instead of that which was in

the

**Note**on the 10th Definition of Book 11th ; besides , the Translation is much ... Side 121

... so let Y be to Z ; + See

to a ; 16 BOOK . v . 121 THE ELEMENTS OF EUCLID . Let the first ratios be those

of A to B...

... so let Y be to Z ; + See

**Note**. * Definition of compound ratio . and K to L , as Zto a ; 16 BOOK . v . 121 THE ELEMENTS OF EUCLID . Let the first ratios be those

of A to B...

Side 177

... meet one another , and are not in the same plane with the other two :

wherefore they contain equal angles ( 10 . 11 . ) ; the angle D * See

therefore equal to the angle DCF ; and 23 BOOK XI . 177 THE ELEMENTS OF

EUCLID .

... meet one another , and are not in the same plane with the other two :

wherefore they contain equal angles ( 10 . 11 . ) ; the angle D * See

**Note**. ABH istherefore equal to the angle DCF ; and 23 BOOK XI . 177 THE ELEMENTS OF

EUCLID .

Side 179

... GE : and because FG is perpendicular to the plane EDC , it makes right angles

( 3 . def . 11 . ) with every straight line meeting * See

therefore each of the BOOK XI . 179 : THE ELEMENTS OF EUCLID . APARNDA ..

.

... GE : and because FG is perpendicular to the plane EDC , it makes right angles

( 3 . def . 11 . ) with every straight line meeting * See

**Note**. A it in that plane :therefore each of the BOOK XI . 179 : THE ELEMENTS OF EUCLID . APARNDA ..

.

Side 184

... straight lines : therefore , because the parallelogram AB is equal to CD ; as the

base AB is to the base LQ , so is ( 7 . 5 . ) the base CD to the same LQ : and

because the solid parallelopiped AR is cut by the plane LMEB , which * See

.

... straight lines : therefore , because the parallelogram AB is equal to CD ; as the

base AB is to the base LQ , so is ( 7 . 5 . ) the base CD to the same LQ : and

because the solid parallelopiped AR is cut by the plane LMEB , which * See

**Note**.

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added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid sphere square square of BC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 36 - 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 at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 145 - 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 65 - 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 248 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 121 - 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 21 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.

Side 80 - 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 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.