## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |

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Side 76

One

the inside or outside . For , if it be possible , let the

in more points than one ; and first on the inside , in the points B , D. H E В.

One

**circle**cannot touch another in more points than one , whether it**touches**it onthe inside or outside . For , if it be possible , let the

**circle**EBF touch the**circle**ABCin more points than one ; and first on the inside , in the points B , D. H E В.

Side 80

The straight line drawn from A at right angles to BA does not fall within the

... From this it is manifest that the straight line which is drawn at right angles to the

diam : ter of a

The straight line drawn from A at right angles to BA does not fall within the

**circle**.... From this it is manifest that the straight line which is drawn at right angles to the

diam : ter of a

**circle**from the extremity of it ,**touches**the**circle**( III . Def . 2. ) ... Side 81

circle ( III . Def . 2. ) ; and that it touches it only in one point , because , if it did

meet the circle in two , it would fall within it ( III . 2. ) . “ Also it is evident that there

can be but one straight line which

circle ( III . Def . 2. ) ; and that it touches it only in one point , because , if it did

meet the circle in two , it would fall within it ( III . 2. ) . “ Also it is evident that there

can be but one straight line which

**touches the circle**in the same point . ” PROP . Side 82

PROP . XVIII . THEOREM . If a straight line touches a circle , the straight line

drawn from the centre to the point of contact , shall be perpendicular to the line

take ( III ...

PROP . XVIII . THEOREM . If a straight line touches a circle , the straight line

drawn from the centre to the point of contact , shall be perpendicular to the line

**touching the circle**. Let the straight line DE touch the circle ABC in the point C ;take ( III ...

Side 94

AD

cuts the circle , ( III . 32. ) 3 . The angle DAB is equal to the angle in the alternate

segment AHB : but the angle DAB is equal ( Constr . ) to the angle C ; therefore ...

AD

**touches the circle**AHB ; and because AB drawn from the point of contact Acuts the circle , ( III . 32. ) 3 . The angle DAB is equal to the angle in the alternate

segment AHB : but the angle DAB is equal ( Constr . ) to the angle C ; therefore ...

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The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Uten tilgangsbegrensning - 1854 |

### Vanlige uttrykk og setninger

ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base base BC bisected centre circle ABC circumference coincide common cuts the circle demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line given triangle greater impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown sides square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle wherefore whole

### Populære avsnitt

Side 26 - 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 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Side 32 - 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 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

Side 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 7 - AB; but things which are equal to the same are equal to one another...

Side 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.

Side 53 - 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.

Side 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 52 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced...