## 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 1-5 av 85

Side 2

... angle is that which is less than a right angle . XIII . A term or boundary is the

extremity of any thing . XIV . A

boundaries . XV . A circle is a plane

ELEMENTS .

... angle is that which is less than a right angle . XIII . A term or boundary is the

extremity of any thing . XIV . A

**figure**is that which is enclosed by one or moreboundaries . XV . A circle is a plane

**figure**contained by AS EUCLID ' SELEMENTS .

Side 3

A circle is a plane

, and is such that all straight lines drawn from a certain point within the

the circumference , are equal to one another . XVI . And this point is called the ...

A circle is a plane

**figure**contained by one line , which is called the circumference, and is such that all straight lines drawn from a certain point within the

**figure**tothe circumference , are equal to one another . XVI . And this point is called the ...

Side 5

All other four - sided

Parallel straight lines are such as are in the same plane , and which being

produced ever so far both ways , do not meet . A . A parallelogram is a four -

sided

All other four - sided

**figures**besides these , are called Trapeziums . XXXV .Parallel straight lines are such as are in the same plane , and which being

produced ever so far both ways , do not meet . A . A parallelogram is a four -

sided

**figure**, of ... Side 29

All the interior angles of any rectilineal

equal to twice as many right angles as the

rectilineal

sides ...

All the interior angles of any rectilineal

**figure**together with four right angles , areequal to twice as many right angles as the

**figure**has sides . EKN в For anyrectilineal

**figure**ABCDE can be divided into as many triangles as the**figure**hassides ...

Side 30

therefore the same angles of these triangles are equal to the angles of the

together with four right angles ; but it has been proved that the angles of the

triangles are equal to twice as many right angles as the

therefore all ...

therefore the same angles of these triangles are equal to the angles of the

**figure**together with four right angles ; but it has been proved that the angles of the

triangles are equal to twice as many right angles as the

**figure**has sides ;therefore all ...

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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.