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

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Resultat 1-5 av 20

Side 9

is

Ax . 8. ) be equal to it . Wherefore also 5 . The whole triangle ABC shall coincide

with the whole triangle DEF and be equal to it ; and the other angles of the one ...

is

**impossible**; therefore 4 . The base BC shall coincide with the base EF , and (Ax . 8. ) be equal to it . Wherefore also 5 . The whole triangle ABC shall coincide

with the whole triangle DEF and be equal to it ; and the other angles of the one ...

Side 12

The angle BDC is equal to the angle BCD ; but it has been demonstrated to be

greater than it , which is

other triangle ACB ; produce AC , AD to E , F ; therefore because AC is equal to ...

The angle BDC is equal to the angle BCD ; but it has been demonstrated to be

greater than it , which is

**impossible**. But if one of the vertices , as D , be within theother triangle ACB ; produce AC , AD to E , F ; therefore because AC is equal to ...

Side 13

... base EF , and upon the same side of it , there can two triangles that have their

sides wbich are terminated in one extremity of the base equal to one another ,

and likewise their sides terminated in the other extremity . But this is

... base EF , and upon the same side of it , there can two triangles that have their

sides wbich are terminated in one extremity of the base equal to one another ,

and likewise their sides terminated in the other extremity . But this is

**impossible**... Side 15

... angle DBE is equal to the angle EB4 ; wherefore ( Ax . 1. ) 3 . The angle DBE is

equal to the angle CBE , the less to the greater , which is

. Two straight lines cannot have a common segment , PROP . XII . - PROBLEM .

... angle DBE is equal to the angle EB4 ; wherefore ( Ax . 1. ) 3 . The angle DBE is

equal to the angle CBE , the less to the greater , which is

**impossible**; therefore 4. Two straight lines cannot have a common segment , PROP . XII . - PROBLEM .

Side 18

The remaining angle ABE is equal to the remaining angle ABD , the less to the

greater , which is

BC . And in like manner it may be demonstrated that no other can be in the same

...

The remaining angle ABE is equal to the remaining angle ABD , the less to the

greater , which is

**impossible**; therefore 4 . BE is not in the same straight line withBC . And in like manner it may be demonstrated that no other can be in the same

...

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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...