## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 14

Side 169

EVERY

four right angles . First , let the

angles BAC , CAD , DAB . These three together are less than four right angles ,

Take in ...

EVERY

**solid**angle is contained by plane angles which together are less thanfour right angles . First , let the

**solid**angle at A be contained by three planeangles BAC , CAD , DAB . These three together are less than four right angles ,

Take in ...

Side 177

the

the figure AF with the figure KP , because they are equal and similar to one

another : therefore the straight lines AE , EF , FB , coincide with KO , OP , PL ; and

the ...

the

**solid**angle at K ; wherefore the plane AF coincides with the plane KP , andthe figure AF with the figure KP , because they are equal and similar to one

another : therefore the straight lines AE , EF , FB , coincide with KO , OP , PL ; and

the ...

Side 179

what multiple soever the base LF is of the base AF , the same multiple is the

LV of the

base HF , the same multiple is the

what multiple soever the base LF is of the base AF , the same multiple is the

**solid**LV of the

**solid**AV : for the same reason , whatever multiple the base NF is of thebase HF , the same multiple is the

**solid**NV of the**solid**ED ; and if the base LF ... Side 184

lelopiped ; but the

opposite parallelogram , is equal ( 29 . 11 . ) to the

the parallelogram ACBL , to which ORQP NK мн A C is the one opposite ...

lelopiped ; but the

**solid**CM , of which the base is ACBL , to which FDHM is theopposite parallelogram , is equal ( 29 . 11 . ) to the

**solid**CP , of which the base isthe parallelogram ACBL , to which ORQP NK мн A C is the one opposite ...

Side 185

the

parallelopiped CR is cut by the plane LMFD , which is parallel to the opposite

planes CP , BR ; as the base CD to the base LQ , so P F R is the

NTME

the

**solid**AE to the**solid**LR : for the same reason , because the**solid**parallelopiped CR is cut by the plane LMFD , which is parallel to the opposite

planes CP , BR ; as the base CD to the base LQ , so P F R is the

**solid**CF to theNTME

**solid**LR ...### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

### Vanlige uttrykk og setninger

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.