## 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 7

**AC is equal**to AB ; and because the point B is the centre of the circle ACE , 2 . BC 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 ... 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 ,

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 two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the ... Side 10

Let ABC be an isosceles triangle , of which the side AB is

Let ABC be an isosceles triangle , of which the side AB is

**equal**to**AC**, and let the straight lines AB ,**AC**, be produced to D and E , the angle ABC shall be**equal**to the angle ACB , and the angle CBD to the angle BCE . Side 11

A D B For if AB be not

A D B For if AB be not

**equal**to**AC**, one of them is greater than the other . Let AB be the greater , and from it cut off ( I. 3. ) DB**equal**to**AC**, the less , and join DČ . Therefore because in the triangles DBC , ACB , DB is**equal**to ... Side 12

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

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