## The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12]. |

### Inni boken

Resultat 6-10 av 79

Side 63

If two straight lines

towards the same parts , when are the

unequal ? 80 . If either diameter of a four - sided figure divide it into two equal

triangles ...

If two straight lines

**join**the extremities of two parallel straight lines , but nottowards the same parts , when are the

**joining**lines equal , and when are theyunequal ? 80 . If either diameter of a four - sided figure divide it into two equal

triangles ...

Side 72

From A draw AF perpendicular to CD , and produce it to E , making FE equal to

AF , and

angles with CD . For since AF is equal to FE , and FG is common to the two

triangles ...

From A draw AF perpendicular to CD , and produce it to E , making FE equal to

AF , and

**join**BE cutting CD in G .**Join**also ÀG . Then AG and BG make equalangles with CD . For since AF is equal to FE , and FG is common to the two

triangles ...

Side 73

Bisect BC ' in E , and

ABC : hence the triangle ABE is equal to the triangle DBF ; take away from these

equals the triangle DBE , therefore the remainder ADE is equal to the ...

Bisect BC ' in E , and

**join**AE , DE , AF , then the triangle ABE is half of the triangleABC : hence the triangle ABE is equal to the triangle DBF ; take away from these

equals the triangle DBE , therefore the remainder ADE is equal to the ...

Side 75

From every point of a given straight line , the straight lines drawn to each of two

given points on opposite sides of the line are equal : prove that the line

the given points will cut the given line at right angles . 17 . If A be the vertex of an

...

From every point of a given straight line , the straight lines drawn to each of two

given points on opposite sides of the line are equal : prove that the line

**joining**the given points will cut the given line at right angles . 17 . If A be the vertex of an

...

Side 80

DH , equal to each other , and

produced of any parallelogram , such that the angle it makes with the line

the point and one extremity of the opposite side , may be bisected by the line

DH , equal to each other , and

**join**AF . ... To find a point in the side or sideproduced of any parallelogram , such that the angle it makes with the line

**joining**the point and one extremity of the opposite side , may be bisected by the line

**joining**it ...### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

ABCD Algebraically Apply base bisected Book chord circle circumference common construction contained definition demonstrated described diagonals diameter difference distance divided double draw drawn equal equal angles equiangular equilateral triangle equimultiples Euclid extremities fall figure formed four fourth Geometrical given circle given line given point given straight line greater half Hence inscribed intersection isosceles join length less Let ABC line drawn magnitudes manner mean meet multiple parallel parallelogram pass perpendicular plane problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio reason rectangle rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid square straight line taken tangent THEOREM third touch triangle ABC twice units vertex wherefore whole

### Populære avsnitt

Side 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.

Side 83 - 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, together with the square...

Side 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...

Side 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Side 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.

Side 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.

Side 81 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.

Side 341 - On the same base, and on the same side of it, there cannot be two triangles...

Side 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.