## 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]. |

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Resultat 1-5 av 81

Side 6

All right angles are equal to one another . XII . If a straight line meets two straight

lines , so as to make the two interior angles on the same side of it taken together

...

All right angles are equal to one another . XII . If a straight line meets two straight

lines , so as to make the two interior angles on the same side of it taken together

**less**than two right angles ; these straight lines being continually produced , shall...

Side 8

1 . ) Wherefore from the given point A , a straight line AL has been drawn equal to

the given straight line BC . Which was to be done . PROPOSITION III . PROBLEM

. From the greater of two given straight lines to cut off a part equal to the

1 . ) Wherefore from the given point A , a straight line AL has been drawn equal to

the given straight line BC . Which was to be done . PROPOSITION III . PROBLEM

. From the greater of two given straight lines to cut off a part equal to the

**less**. Side 11

If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the

equal to AC , and BC is common to both triangles , the two sides DB , B Care

equal to ...

If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the

**less**, ( 1 . 3 . ) and join DC . Then , in the triangles DBC , ABC , because DB isequal to AC , and BC is common to both triangles , the two sides DB , B Care

equal to ...

Side 18

Then any two of its angles together shall be

Produce any side BC to D . Then because ACD is the exterior angle of the

triangle ABC ; therefore the angle ACD is greater than the interior and opposite

angle ABC ...

Then any two of its angles together shall be

**less**than two right angles . с рProduce any side BC to D . Then because ACD is the exterior angle of the

triangle ABC ; therefore the angle ACD is greater than the interior and opposite

angle ABC ...

Side 19

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

AB ; if AC were equal to AB , then the angle ABC would be equal to the angle

ACB ; ( 1 . 5 . ) but it is not equal ; ( hyp . ) therefore the side AC is not equal to AB

.

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

**less**thanAB ; if AC were equal to AB , then the angle ABC would be equal to the angle

ACB ; ( 1 . 5 . ) but it is not equal ; ( hyp . ) therefore the side AC is not equal to AB

.

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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.