## 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 shown that BC is equal to BG ;

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 9

The point B shall coincide with the point E , because AB is equal to DE . And AB coinciding with DE , 2 . AC shall coincide with DF , because the angle BAC ' is equal to the angle EDF ;

The point B shall coincide with the point E , because AB is equal to DE . And AB coinciding with DE , 2 . AC shall coincide with DF , because the angle BAC ' is equal to the angle EDF ;

**wherefore**also 3 . The point C shall coincide with ... Side 11

**Wherefore**, if two angles , & c . Q.E.D , COR . — Hence every equiangular triangle is also equilateral . PROP . VII . -THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which ... Side 12

The angles ECD , FDC , are equal to one another ; but the angle ECD is greater than the angle BCD ;

The angles ECD , FDC , are equal to one another ; but the angle ECD is greater than the angle BCD ;

**wherefore**likewise 2 . The angle FDC is greater than BCD ; much more then 3 . The angle BDC is greater than the angle BCD . Side 13

therefore , if the base BC coincide with the base EF , the sides BA , ÁC , cannot but coincide with the sides ED , DF ;

therefore , if the base BC coincide with the base EF , the sides BA , ÁC , cannot but coincide with the sides ED , DF ;

**wherefore**likewise 3 . The angle BAC coincides with the angle EDF , and is equal ( Ax . 8. ) to it .### 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...