## The Elements of Euclid |

### Inni boken

Side 12

Therefore ,

Therefore ,

**if two**triangles have**two sides**of the one equal to**two sides**of the**other**, each to each , and have likewise ... Let ABC be an isosceles triangle , of which the**side**AB is equal to AC , and let the**straight lines**AB , AC be ... Side 18

Wherefore ,

Wherefore ,

**when**a**straight line**, & c . Q. E. D. PROP . XIV . THEOR . Ip , at a**point**in a**straight line**,**two other straight lines**,**upon**the**opposite sides**of it ,**make**the adjacent angles together equal to**two**right angles , these ... Side 26

Therefore ,

Therefore ,

**if two**triangles , & c . Q. E. D. PROP . XXVII . THEOR . Ir a**straight line**falling**upon two other straight lines makes**the alternate**angles**equal to one**another**, these**two straight lines**shall be parallel . Side 36

to

to

**two**right**angles**: wherefore the**angles**BHF , HFE are less than**two**right**angles**: but**straight lines**which with**another straight line make**the interior**angles upon**the same**side**less than**two**right**angles**,**do**meet ( 12 . Ax . )**if**... Side 38

the G

the G

**two straight lines**AC , AG**upon**the**opposite sides**of AB ,**make**with it at the**point**A the adjacent angles equal to**two**right angles : F therefore CA is in the same K**straight line**( 14. 1. ) with AG : for the same reason , AB and ...### Hva folk mener - Skriv en omtale

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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 34 - 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 143 - 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 63 - 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 246 - 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 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 119 - 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 19 - 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 12 - 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 78 - 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 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.