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

### Inni boken

Resultat 1-5 av 56

Side 11

sides also which subtend , or are opposite to , the equal angles , shall be equal to

...

**Q.E.D.**COROLLARY . - Hence every equilateral triangle is also equiangular .**PROP**. VI . - THEOREM . If two angles of a triangle be equal to one another , thesides also which subtend , or are opposite to , the equal angles , shall be equal to

...

Side 12

to two sides of the other , each to each , and have likewise their bases equal ; the

angle which is contained by the two sides of the one shall be equal to the angle ...

**Q.E.D. PROP**. VIII . - THEOREM . If two triangles have two sides of the one equalto two sides of the other , each to each , and have likewise their bases equal ; the

angle which is contained by the two sides of the one shall be equal to the angle ...

Side 13

divide it into two equal angles . Let BAC be the given rectilineal angle , it is

required to bisect it . Take any point D'in AB , and from 8C cut ( I. 3. ) off AE equal

to AD ...

**Q.E.D. PROP**. IX . - PROBLEM . To bisect a given rectilineal angle , that is , todivide it into two equal angles . Let BAC be the given rectilineal angle , it is

required to bisect it . Take any point D'in AB , and from 8C cut ( I. 3. ) off AE equal

to AD ...

Side 17

lines , upon the opposite sides of it , make the adjacent angles together equal to

two right angles , these two straight lines shall be in one and the same straight ...

**Q.E.D. PROP**. XIV . - THEOREM . If at a point in a straight line , two other straightlines , upon the opposite sides of it , make the adjacent angles together equal to

two right angles , these two straight lines shall be in one and the same straight ...

Side 18

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

straight line with it but BD , therefore 5 . BD is in the same straight line with CB .

Wherefore , if at a point , & c .

lines cut ...

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

straight line with it but BD , therefore 5 . BD is in the same straight line with CB .

Wherefore , if at a point , & c .

**Q.E.D. PROP**. XV . - THEOREM . If two straightlines cut ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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...