## Elements of geometry, based on Euclid, books i-iii |

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Resultat 1-5 av 7

Side 56

If the sides of a triangle be such that they are respectively the sum of two given

lines , the difference of the same two lines , and

to the

If the sides of a triangle be such that they are respectively the sum of two given

lines , the difference of the same two lines , and

**twice**the side of a square equalto the

**rectangle**contained by these lines , the triangle shall be right - angled ... Side 64

AD · DB The rectangle AD , DB , together with tho square on CB , shall be equal

to the square on CD . ... and on one of the parts are equal to

contained by the whole and that part , together with the square on the other part .

AD · DB The rectangle AD , DB , together with tho square on CB , shall be equal

to the square on CD . ... and on one of the parts are equal to

**twice the rectangle**contained by the whole and that part , together with the square on the other part .

Side 65

But

cor . ) ; Therefore the gnomon AKF , together with the square CK , is equal to

the ...

But

**twice the rectangle**AB , BC is also double of AK , for BK is equal to BC ( II . 4 ,cor . ) ; Therefore the gnomon AKF , together with the square CK , is equal to

**twice the rectangle**AB , BC . To each of these equals add HF , which is equal tothe ...

Side 72

AB , Therefore the rectangle CF , FA , together with the square on AE , is equal to

the squares on AE and AB . Take away the square ... The square on AB shall be

greater than the squares on AC and CB by

AB , Therefore the rectangle CF , FA , together with the square on AE , is equal to

the squares on AE and AB . Take away the square ... The square on AB shall be

greater than the squares on AC and CB by

**twice the rectangle**BC , CD . Proof . Side 73

BD2 + DAS squares on BC , CD , DA , and

the square on BA is equal to the squares on BD and ( CD + DA , because the

angle at D is a right angle ( I . 47 ) ; And the square on CA is equal to the squares

...

BD2 + DAS squares on BC , CD , DA , and

**twice the rectangle**BC , CD . FEB Butthe square on BA is equal to the squares on BD and ( CD + DA , because the

angle at D is a right angle ( I . 47 ) ; And the square on CA is equal to the squares

...

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Elements of Geometry, Based on Euclid, Bøker 1-3 Edward Atkins Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD angle ABC angle BAC angle BCD angle equal base BC BC is equal bisect centre chord circle ABC circumference coincide common Const CONSTRUCTION cqual describe diagonal diameter difference divided double draw drawn equal to CD equal to twice exterior angle extremities fall figure four given point given rectilineal given straight line gnomon greater impossible join length less Let ABC Let the straight manner meet opposite angles parallel parallelogram pass perpendicular possible produced PROOF PROOF.—Because Proposition proved rectangle contained right angles segment semicircle shown side BC sides square on AC Take taken third touches the circle triangle ABC twice the rectangle unequal whole

### Populære avsnitt

Side 35 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.

Side 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.

Side 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 17 - If two triangles have two sides of the one equal to two sides of the...

Side 51 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.

Side 9 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.

Side 32 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.

Side 67 - 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 of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.