## 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 23

Side 28

If a straight line ,

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

line EF , which

angles ...

If a straight line ,

**falling**upon two other straight lines , make the alternate anglesequal to one another , these two straight lines shall be parallel . Let the straight

line EF , which

**falls**upon the two straight lines AB , CD , make the alternateangles ...

Side 29

Let the straight line EF

angles AGH , GHD , are equal to one another ; and the exterior angle EG B is

equal to the interior and opposite , upon the same side , GHD ; and the two

interior ...

Let the straight line EF

**fall**upon the parallel straight lines AB , CD ; the alternateangles AGH , GHD , are equal to one another ; and the exterior angle EG B is

equal to the interior and opposite , upon the same side , GHD ; and the two

interior ...

Side 30

but those straight lines which , with another straight line

the interior angles on the same side less than two right angles , will meet ( Ax . 12

. ) together if continually produced ; therefore 3 . The straight lines AB , CD ...

but those straight lines which , with another straight line

**falling**upon them , makethe interior angles on the same side less than two right angles , will meet ( Ax . 12

. ) together if continually produced ; therefore 3 . The straight lines AB , CD ...

Side 31

Again , because AB is parallel to CE , and BD

angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE

was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3 . The whole

exterior ...

Again , because AB is parallel to CE , and BD

**falls**upon them , 2 . The exteriorangle ECD is equal to the interior and opposite angle ABC ; but the angle ACE

was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3 . The whole

exterior ...

Side 41

Then because the straight line HF

The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9.

) 2 . The angles BHF , HFE , are less than two right angles ; but ( Ax . 12. ) ...

Then because the straight line HF

**falls**upon the parallels AH , EF , ( I. 29. ) 1 .The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9.

) 2 . The angles BHF , HFE , are less than two right angles ; but ( Ax . 12. ) ...

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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...