## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 11

Side 143

BCD equal to the angle ECG : the ratio of the

their sides . Let BG , CG , be placed in a straight line ; therefore DC and CE are

also in a ...

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 of the ratios oftheir sides . Let BG , CG , be placed in a straight line ; therefore DC and CE are

also in a ...

Side 145

to the

equal to D ; and it is similar to ABC . Therefore ... If two similar

have a common angle , and be similarly situated , they are about the same

diameter .

to the

**parallelogram**EF : but EF is equal to the figure D ; wherefore also KGH isequal to D ; and it is similar to ABC . Therefore ... If two similar

**parallelograms**have a common angle , and be similarly situated , they are about the same

diameter .

Side 147

To a given straight line to apply a

, and deficient by a

rectilineal figure to which the

To a given straight line to apply a

**parallelogram**equal to a given rectilineal figure, and deficient by a

**parallelogram**similar to a given**parallelogram**: but the givenrectilineal figure to which the

**parallelogram**to be applied is to be equal , must ... Side 177

Ir a solid be contained by six planes , two and two of which are parallel ; the

opposite planes are similar and equal

contained by the parallel planes AC , GF ; BG , CE ; FB , AE : its opposite planes

are ...

Ir a solid be contained by six planes , two and two of which are parallel ; the

opposite planes are similar and equal

**parallelograms**. * Let the solid CDGH becontained by the parallel planes AC , GF ; BG , CE ; FB , AE : its opposite planes

are ...

Side 184

lelopiped ; but the solid CM , of which the base is ACBL , to which FDHM is the

opposite

the

lelopiped ; but the solid CM , of which the base is ACBL , to which FDHM is the

opposite

**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 ...### 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.