## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

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Side 21

... to that of the triangle (4.1.)ACB, the less to the greater; which is absurd.

Therefore, AB is not unequal to AC, that is, it is equal to it. Wherefore, if two

angles, &c.

equilateral. -4

... to that of the triangle (4.1.)ACB, the less to the greater; which is absurd.

Therefore, AB is not unequal to AC, that is, it is equal to it. Wherefore, if two

angles, &c.

**Q. E. D.**B C CoR. Hence every equiangular triangle is alsoequilateral. -4

**PROP**... Side 22

two . sides of the other, each to each, and have likewise their bases equal; the

angle which is contained by the two sides of the one shall be equal to the angle ...

**Q. E. D.**- -**PROP**. VIII. THEOR. If two triangles have two sides of the one equal totwo . sides of the other, each to each, and have likewise their bases equal; the

angle which is contained by the two sides of the one shall be equal to the angle ...

Side 23

... wherefore likewise the angle BAC coincides with the angle EDF, and is equal (

8. Ax.) to it. Therefore if two triangles, &c.

e e - To bisect a given rectilineal angle, that is, to divide it * into two equal angles.

... wherefore likewise the angle BAC coincides with the angle EDF, and is equal (

8. Ax.) to it. Therefore if two triangles, &c.

**Q. E. D.**- so**PROP**. IX. PROB. - • * --- -e e - To bisect a given rectilineal angle, that is, to divide it * into two equal angles.

Side 26

straight lines, upon the opposite sides of it, make the adjacent angles together

equal to two right angles, these two straight lines are in one and the same

straight line.

**Q. E. D.**. a**PROP**. XIV. THEOR. . . . If, at a point in a straight line, two otherstraight lines, upon the opposite sides of it, make the adjacent angles together

equal to two right angles, these two straight lines are in one and the same

straight line.

Side 28

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

less A. than two right angles. Produce BC to D ; and because ACD is the exterior

...

**Q. E. D.**-**PROP**. xvii. THEOR. Any two angles of a triangle are together less thantwo right angles. - Let ABC be any triangle; any - two of its angles together are

less A. than two right angles. Produce BC to D ; and because ACD is the exterior

...

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclides,John Playfair Uten tilgangsbegrensning - 1826 |

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### Vanlige uttrykk og setninger

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition pyramid Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore

### Populære avsnitt

Side 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.

Side 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Side 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.

Side 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.

Side 30 - 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 other two sides of the triangle, but shall contain a greater angle.

Side 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.

Side 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.

Side 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.