## 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 32

Side 5

XXXV .

being produced ever so far both ways , do not meet . POSTULATES . I. Let it be

granted that a straight line may be drawn from any one point to any other point . II

.

XXXV .

**Parallel**straight lines are such as are in the same plane , and which ,being produced ever so far both ways , do not meet . POSTULATES . I. Let it be

granted that a straight line may be drawn from any one point to any other point . II

.

Side 28

A E B G C T D For , if it be not

either towards B , D , or towards A , C ; let them be produced and meet towards B

, D , in the point G ; therefore 1 . GEF is a triangle , and its exterior angle AEF is ...

A E B G C T D For , if it be not

**parallel**, AB and CD being produced , shall meeteither towards B , D , or towards A , C ; let them be produced and meet towards B

, D , in the point G ; therefore 1 . GEF is a triangle , and its exterior angle AEF is ...

Side 29

AB is

to two right angles , and that AGH , BGH , are also equal ( I. 13. ) to two right

angles , 1 . The angles AGH , BGH , are equal to the angles BGH , GHD Take

away ...

AB is

**parallel**to CD . Again , because the angles BGH , GHD , are equal ( Hyp . )to two right angles , and that AGH , BGH , are also equal ( I. 13. ) to two right

angles , 1 . The angles AGH , BGH , are equal to the angles BGH , GHD Take

away ...

Side 30

The straight lines AB , CD , shall meet , if produced far enough ; but they never

meet , since they are

not unequal to the angle GHD , that is , it is equal to it ; but ( I. 15. ) the angle AGH

is ...

The straight lines AB , CD , shall meet , if produced far enough ; but they never

meet , since they are

**parallel**by the hypothesis ; therefore 4 . The angle AGH isnot unequal to the angle GHD , that is , it is equal to it ; but ( I. 15. ) the angle AGH

is ...

Side 31

To draw a straight line through a given point

A be the given point , and BC the given straight line ; it is required to draw a

straight line through the point A ,

point ...

To draw a straight line through a given point

**parallel**to a given straight line . LetA be the given point , and BC the given straight line ; it is required to draw a

straight line through the point A ,

**parallel**to the straight line BC . In BC take anypoint ...

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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...