## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

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Side 12

one side of it , are either two right angles , or are together equal to two right

angles . Let the straight line AB make with CD , upon one side of it the angles

CBA ...

**PROP**. VI . THEOR . The angles which one straight line makes with another uponone side of it , are either two right angles , or are together equal to two right

angles . Let the straight line AB make with CD , upon one side of it the angles

CBA ...

Side 13

... may be demonstrated , that no other can be in the same straight line with it but

BD , which therefore is in the same straight line with CB . B

. If two straight lines cut one another , the vertical , or opposite angles are equal .

... may be demonstrated , that no other can be in the same straight line with it but

BD , which therefore is in the same straight line with CB . B

**PROP**. VIII . THEOR .. If two straight lines cut one another , the vertical , or opposite angles are equal .

Side 15

greater side , or has the greater side opposite to it . Let ABC be a triangle , of

which the angle ABC is greater than the angle BCA ; the side AČ is likewise

greater than ...

**PROP**. XII . THEOR . The greater angle of every triangle is subtended by thegreater side , or has the greater side opposite to it . Let ABC be a triangle , of

which the angle ABC is greater than the angle BCA ; the side AČ is likewise

greater than ...

Side 17

... of the triangle EFG is greater than its angle EGF , and because the greater ( 12.

1. ) side is opposite to the greater angle , the side EG is greater than the side EF ;

but EG is equal to BC ; and therefore also BC is greater than EF .

... of the triangle EFG is greater than its angle EGF , and because the greater ( 12.

1. ) side is opposite to the greater angle , the side EG is greater than the side EF ;

but EG is equal to BC ; and therefore also BC is greater than EF .

**PROP**. XVI . Side 18

1

from a point , situated without a straight line , to that line : any two oblique lines

drawn from the same point on different sides of the perpendicular , cutting off

equal ...

1

**PROP**. XVII . THEOR . A perpendicular is the shortest line that can be drawnfrom a point , situated without a straight line , to that line : any two oblique lines

drawn from the same point on different sides of the perpendicular , cutting off

equal ...

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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid spherical square straight line taken tangent THEOR third touch triangle ABC wherefore whole