## 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

Side 7

To describe an equilateral triangle upon a

one of the points in which the circles cut one another , draw the straight

...

To describe an equilateral triangle upon a

**given**finite straight**line**. Let AB be the**given**straight**line**. ... at the distance BA , describe the circle ACE ; and from C ,one of the points in which the circles cut one another , draw the straight

**lines**CA...

Side 14

To draw a straight

in the same . Let AB be the

required to draw a straight

AC ...

To draw a straight

**line**at right angles to a**given**straight**line**, from a**given**pointin the same . Let AB be the

**given**straight**line**, and C a**given**point in it . It isrequired to draw a straight

**line**from the point C at right angles to AB . B D C E InAC ...

Side 22

therefore the three straight

A , B , C : and therefore the triangle KFG has its three ... At a

straight

therefore the three straight

**lines**KF , FG , GK , are respectively equal to the three ,A , B , C : and therefore the triangle KFG has its three ... At a

**given**point in a**given**straight

**line**, to make a rectilineal angle equal to a**given**rectilineal angle . Side 28

Straight

other . Let the straight

AB be ... PROBLEM . To draw a straight

Straight

**lines**which are parallel to the same straight**line**are parallel to eachother . Let the straight

**lines**AB , CD , be each of them parallel to EF . Then shallAB be ... PROBLEM . To draw a straight

**line**through a**given**point parallel to a**given**... Side 38

Therefore to the

equal to the triangle C , and having the angle ABM equal to the

. E . F . PROPOSITION XLV . PROBLEM . To describe a parallelogram equal to a

...

Therefore to the

**given**straight**line**AB , the parallelogram LB has been applied ,equal to the triangle C , and having the angle ABM equal to the

**given**angle D . Q. E . F . PROPOSITION XLV . PROBLEM . To describe a parallelogram equal to a

...

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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.