## 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 38

Side 7

From the

1. ) the equilateral triangle DAB , and produce ( Post . 2. ) the straight lines DĂ ,

DB to E and

From the

**point**A to B draw ( Post . I. ) the straight line 4B ; and upon it describe ( I.1. ) the equilateral triangle DAB , and produce ( Post . 2. ) the straight lines DĂ ,

DB to E and

**F**. From the centre B at the distance BC , describe ( Post . 3. ) ... Side 9

But the

with the base EF ; because , the

base BC does not coincide with the base EF , two straight lines would inclose a ...

But the

**point**B coincides with the**point**E ; wherefore the base BC shall coincidewith the base EF ; because , the

**point**B coinciding with E , and C with**F**, if thebase BC does not coincide with the base EF , two straight lines would inclose a ...

Side 10

А B В F G D E In BD take any

( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to AG ,

and AB ( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB ...

А B В F G D E In BD take any

**point F**, and from AE , the greater , cut off AG equal( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to AG ,

and AB ( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB ...

Side 13

А D G B D For if the triangle ABC be applied to DEF , so that the point B be on E ,

and the straight line BC upon EF ; 1 . The point C shall coincide with the

because BC is equal to EF ; therefore BC coinciding with EF , 2 . BA and AC ...

А D G B D For if the triangle ABC be applied to DEF , so that the point B be on E ,

and the straight line BC upon EF ; 1 . The point C shall coincide with the

**point F**,because BC is equal to EF ; therefore BC coinciding with EF , 2 . BA and AC ...

Side 15

straight line FC drawn from the given

straight line AB

triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC , CF ,

each to ...

straight line FC drawn from the given

**point**C is at right angles to the givenstraight line AB

**F**А с E B Because DC is equal CE , and FC common to the twotriangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC , CF ,

each to ...

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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...