## 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 32

Side 153

X . An arc of a circle is any portion of the circumference ; and a

straight line joining the extremities of an arc . Every

divides a circle into two unequal segments , one greater than , and the other less

than a ...

X . An arc of a circle is any portion of the circumference ; and a

**chord**is thestraight line joining the extremities of an arc . Every

**chord**except a diameterdivides a circle into two unequal segments , one greater than , and the other less

than a ...

Side 157

Euclid departs from the ordinary ex absurdo mode of proof of converse

propositions . QUESTIONS ON BOOK III . 1 . DEFINE accurately the terms radius ,

arc , circumference ,

segment ...

Euclid departs from the ordinary ex absurdo mode of proof of converse

propositions . QUESTIONS ON BOOK III . 1 . DEFINE accurately the terms radius ,

arc , circumference ,

**chord**, secant . 2 . How does a sector differ in form from asegment ...

Side 158

Two parallel

and one inch apart ; how many inches is the diameter in length : 16 . Which is the

greater

Two parallel

**chords**in a circle are respectively six and eight inches in length ,and one inch apart ; how many inches is the diameter in length : 16 . Which is the

greater

**chord**in a circle whose diameter is 10 inches ; that whose length is 5 ... Side 161

PROPOSITION III . THEOREM . If a

produced be equal to the radius , and if from its extremity a line be drawn through

the center and meeting the conver and concave circumferences , the convex is

one ...

PROPOSITION III . THEOREM . If a

**chord**of a circle be produced till the partproduced be equal to the radius , and if from its extremity a line be drawn through

the center and meeting the conver and concave circumferences , the convex is

one ...

Side 162

Wherefore the circumference AE is treble of the circumference BF , and BF is one

- third of AE . Hence may be solved the following problem : AE , BF are two arcs

of a circle intercepted between a

Wherefore the circumference AE is treble of the circumference BF , and BF is one

- third of AE . Hence may be solved the following problem : AE , BF are two arcs

of a circle intercepted between a

**chord**and a given diameter . Determine the ...### 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.