## 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 19

And consequently that all the angles made by any number of lines meeting in

one point are together equal to four right angles . PROP . XVI . - THEOREM . If

one side of a triangle be produced , the

...

And consequently that all the angles made by any number of lines meeting in

one point are together equal to four right angles . PROP . XVI . - THEOREM . If

one side of a triangle be produced , the

**exterior angle**is greater than either of the...

Side 20

Let ABC be any triangle ; any two of its angles together are less than two right

angles . А C B D Produce BC to D ; and because ACD is the

triangle ABC , ( I. 16. ) 1 . ACD is greater than the interior and opposite angle

ABC ...

Let ABC be any triangle ; any two of its angles together are less than two right

angles . А C B D Produce BC to D ; and because ACD is the

**exterior angle**of thetriangle ABC , ( I. 16. ) 1 . ACD is greater than the interior and opposite angle

ABC ...

Side 23

Again , because the

opposite angle ( I. 16. ) 1 . The

than CED . For the same reason , 2 . The

is ...

Again , because the

**exterior angle**of a triangle is greater than the interior andopposite angle ( I. 16. ) 1 . The

**exterior angle**BDC of the triangle CDE is greaterthan CED . For the same reason , 2 . The

**exterior angle**CEB of the triangle ABEis ...

Side 27

The angle BHA is equal to the angle EFD ; but EFD is equal ( Hyp . ) to the angle

BCA ; therefore also 4 . The angle BHA is equal to the angle BCA , that is , the

...

The angle BHA is equal to the angle EFD ; but EFD is equal ( Hyp . ) to the angle

BCA ; therefore also 4 . The angle BHA is equal to the angle BCA , that is , the

**exterior angle**BHA of the triangle AHC is equal to its interior and opposite angle...

Side 28

If a straight line , falling upon two other straight lines , make the alternate angles

equal to one another , these two straight lines shall be parallel . Let the straight

line EF ... GEF is a triangle , and its

...

If a straight line , falling upon two other straight lines , make the alternate angles

equal to one another , these two straight lines shall be parallel . Let the straight

line EF ... GEF is a triangle , and its

**exterior angle**AEF is greater ( I. 16. ) than the...

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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...