## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |

### Inni boken

Resultat 6-10 av 37

Side 18

The remaining angle ABE is equal to the remaining angle ABD , the

The remaining angle ABE is equal to the remaining angle ABD , the

**less**to the greater , which is impossible ; therefore 4 . BE is not in the same straight line with BC . And in like manner it may be demonstrated that no other can be in ... Side 20

Let ABC be any triangle ; any two of its angles together are

Let ABC be any triangle ; any two of its angles together are

**less**than two right angles . А C B D Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1 . ACD is greater than the interior and opposite ... Side 21

B For if it be not greater , AC must either be equal to AB , or

B For if it be not greater , AC must either be equal to AB , or

**less**than it ; it is not equal , because then the angle ABC would be equal ( I. 5. ) to the angle ACB ; but it is not ; therefore 1 . AC is not equal to AB ; neither is it ... Side 22

... CA , are greater than AB . Therefore any two sides , & c . Q.E.D. PROP . XXI . -THEOREM . If from the ends of the side of a triangle , there be drawn two straight lines to a point within the triangle , these shall be

... CA , are greater than AB . Therefore any two sides , & c . Q.E.D. PROP . XXI . -THEOREM . If from the ends of the side of a triangle , there be drawn two straight lines to a point within the triangle , these shall be

**less**than the ... Side 26

For if it be not greater , it must either be equal to it , or

For if it be not greater , it must either be equal to it , or

**less**; but the angle BAC is not equal to the angle EDF , because then the base BC would be equal ( I. 4. ) to EF ; but it is not , therefore 1 . The angle BAC is not equal to ...### Hva folk mener - Skriv en omtale

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The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... EUCLID.,Samuel A. GOOD Uten tilgangsbegrensning - 1854 |

The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... EUCLID.,Samuel A. GOOD Ingen forhåndsvisning tilgjengelig - 1854 |

### Vanlige uttrykk og setninger

ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles equal Constr 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 produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown side BC sides square of AC straight line AC 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...