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

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Resultat 1-5 av 10

Side 14

FC = C3 Therefore the base FC is equal to the base GB ( I . 4 ) ; And the triangle

AFC to the triangle AGB ( I . 4 ) ; And the remaining angles of the one are equal to

the = remaining angles of the other , cach to cach , to which the 2 Arc =

FC = C3 Therefore the base FC is equal to the base GB ( I . 4 ) ; And the triangle

AFC to the triangle AGB ( I . 4 ) ; And the remaining angles of the one are equal to

the = remaining angles of the other , cach to cach , to which the 2 Arc =

**cqual**... Side 22

Proposition 14 . - Theorem . If , at a point in a straight line , two other straight lines

, upon the opposite sides of it , make the adjacent angles together

right angles , these two straight lines shall be in one and the same straight line .

Proposition 14 . - Theorem . If , at a point in a straight line , two other straight lines

, upon the opposite sides of it , make the adjacent angles together

**cqual**to tworight angles , these two straight lines shall be in one and the same straight line .

Side 27

Let ABC be a triangle ; Any two sides of it are together greater than the third side .

CONSTRUCTION . - Produce BA to the point D , making AD C .

) , and join DC . PROOF . - Because DA is equal to AC , the angle ADC is equal ...

Let ABC be a triangle ; Any two sides of it are together greater than the third side .

CONSTRUCTION . - Produce BA to the point D , making AD C .

**cqual**to AC ( I . 3) , and join DC . PROOF . - Because DA is equal to AC , the angle ADC is equal ...

Side 42

But straight lines which join the extremities of

towards the same parts , are themselves .

BE , CH are both equal and parallel ; Therefore EBCH is a parallelogram ( Def .

But straight lines which join the extremities of

**cqual**and parallel straight linestowards the same parts , are themselves .

**cqual**and parallel ( I . 33 ) ; ThereforeBE , CH are both equal and parallel ; Therefore EBCH is a parallelogram ( Def .

Side 49

It is required to describe a parallelogram equal to ABCD , and having an angle

equal to E . CONSTRUCTION . — Join DB . Describe the parallelogram FH equal

to the triangle ADB , and having the angle FKH

It is required to describe a parallelogram equal to ABCD , and having an angle

equal to E . CONSTRUCTION . — Join DB . Describe the parallelogram FH equal

to the triangle ADB , and having the angle FKH

**cqual**to the angle E ( I . 42 ) .### Hva folk mener - Skriv en omtale

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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.