## 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 59

Side 7

is equal to BA . But it has been proved that CA is equal to AB ; therefore CA , CB ,

are each of them equal to AB ; but things which are equal to the same are ...

**AC is equal**to AB ; and because the point B is the centre of the circle ACE , 2 . BCis equal to BA . But it has been proved that CA is equal to AB ; therefore CA , CB ,

are each of them equal to AB ; but things which are equal to the same are ...

Side 9

shall be equal , each to each , viz . those to which the equal sides are opposite .

Let ABC , DEF be two triangles which have the two sides AB ,

sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC ...

shall be equal , each to each , viz . those to which the equal sides are opposite .

Let ABC , DEF be two triangles which have the two sides AB ,

**AC equal**to the twosides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC ...

Side 10

The angles at the base of an isosceles triangle are

the

The angles at the base of an isosceles triangle are

**equal**to one another ; and ifthe

**equal**sides be produced , the angles upon the other side of the base shall be**equal**. Let ABC be an isosceles triangle , of which the side AB is**equal**to**AC**... Side 11

Let ABC be a triangle having the angle ABC

is also

greater than the other . Let AB be the greater , and from it cut off ( I. 3. ) DB

...

Let ABC be a triangle having the angle ABC

**equal**to the angle ACB ; the side ABis also

**equal**to the side**AC**. A D B For if AB be not**equal**to**AC**, one of them isgreater than the other . Let AB be the greater , and from it cut off ( I. 3. ) DB

**equal**...

Side 12

Then , in the case in which the vertex of each of the triangles is without the other

triangle , because

angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ;

therefore ...

Then , in the case in which the vertex of each of the triangles is without the other

triangle , because

**AC is equal**to AD , ( I. 5. ) 1 . The angle ACD is equal to theangle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ;

therefore ...

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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...