## 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 8

But it has been

But it has been

**shown**that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 4 . The straight line AL is equal to BC . Side 21

... and it has been

... and it has been

**shown**that it is not equal to AB ; therefore 3 . AC is greater than AB . Wherefore the greater angle , & c . Q.E.D. PROP . XX . THEOREM . Any two sides of a triangle are together greater than the third side . Side 23

The sides CE , EB , are greater than CD , DB ; but it has been

The sides CE , EB , are greater than CD , DB ; but it has been

**shown**that BA , AC , are greater than BE , EC ; much more then 5 . BA , AC , are greater than BD , DC . Again , because the exterior angle of a triangle is greater than the ... Side 26

The angle BAC is not less than the angle EDF ; and it was

The angle BAC is not less than the angle EDF ; and it was

**shown**that it is not equal to it ; therefore 3 . The angle BAC is greater than the angle EDF . Wherefore if two triangles , & c . Q.E.D. PROP . XXVI . - THEOREM . Side 30

The angle GHF is equal to the angle GKD ; and it was

The angle GHF is equal to the angle GKD ; and it was

**shown**that the angle AGK is equal to the angle GHF ; therefore also 3 . AGK is equal to GKD ; and they are alternate angles ; therefore ( I. 27. ) 4 . AB is parallel to CD .### 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 demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line given triangle gnomon 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...