## 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 27

Side 13

To

BAC be the given rectilineal angle , it is required to

AB , and from 8C cut ( I. 3. ) off AE equal to AD ; join DE , and upon it , on the side

...

To

**bisect**a given rectilineal angle , that is , to divide it into two equal angles . LetBAC be the given rectilineal angle , it is required to

**bisect**it . Take any point D'inAB , and from 8C cut ( I. 3. ) off AE equal to AD ; join DE , and upon it , on the side

...

Side 14

The angle BAC is

. X. - PROBLEM . To

equal parts . Let AB be the given straight line ; it is required to divide it into two ...

The angle BAC is

**bisected**by the straight line AF . Which was to be done . PROP. X. - PROBLEM . To

**bisect**a given finite straight line , that is , to divide it into twoequal parts . Let AB be the given straight line ; it is required to divide it into two ...

Side 16

It is required to draw a straight line perpendicular to AB from the point C. Take

any point Dupon the other side of AB , and from the centre C , at the distance CD ,

describe ( Post . 3. ) the circle EGF meeting . AB in F , G ; and

It is required to draw a straight line perpendicular to AB from the point C. Take

any point Dupon the other side of AB , and from the centre C , at the distance CD ,

describe ( Post . 3. ) the circle EGF meeting . AB in F , G ; and

**bisect**( I. 10. ) ... Side 19

In the same manner , if the side BC be

angle BCG that is ( I. 15. ) 6 . The angle ACD is greater than the angle ABC .

Therefore if one side , & c . Q.E.D. PROP . XVII . - THEOREM . Any two angles

BOOK ...

In the same manner , if the side BC be

**bisected**, it may be demonstrated that theangle BCG that is ( I. 15. ) 6 . The angle ACD is greater than the angle ABC .

Therefore if one side , & c . Q.E.D. PROP . XVII . - THEOREM . Any two angles

BOOK ...

Side 39

Let ABC be the given triangle , and D the given rectilineal angle . It is required to

describe a parallelogram that shall be equal to the given triangle ABC , and have

one of its angles equal to D.

Let ABC be the given triangle , and D the given rectilineal angle . It is required to

describe a parallelogram that shall be equal to the given triangle ABC , and have

one of its angles equal to D.

**Bisect**( I. 10. ) BC in E , join AE , and at the point E ...### Hva folk mener - Skriv en omtale

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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...