## Euclid's Elements [book 1-6] with corrections, by J.R. Young |

### Inni boken

Resultat 1-5 av 6

Side 47

1 . and join E , °C . The triangle ABC is equal * to the triangle EBC , because they

are upon the same base BC , and between the same parallels BC , AE : but the

triangle ABC is * Hyp . equalt to the triangle DBC ; there+ 1 AX .

1 . and join E , °C . The triangle ABC is equal * to the triangle EBC , because they

are upon the same base BC , and between the same parallels BC , AE : but the

triangle ABC is * Hyp . equalt to the triangle DBC ; there+ 1 AX .

**fore**also the ... Side 53

... are right angles ; for , since the straight line XD meets the parallels AB , DE ,

the angles A B * 90 , BAD , ADE are equal " to two Come right angles : but BAD is

at right angle ; there+ 3 Ax .

... are right angles ; for , since the straight line XD meets the parallels AB , DE ,

the angles A B * 90 , BAD , ADE are equal " to two Come right angles : but BAD is

at right angle ; there+ 3 Ax .

**fore**also ADE is at right angle : but the opposite * 34 . Side 65

1 . is equal * to PL , because tbey are * 13 . 1 . the complements of tbe

parallelogram ML ; where+ 1 AX .

rectangles AG , MP , PL , RF , are equal to one another , and so are quadruple of

one of ...

1 . is equal * to PL , because tbey are * 13 . 1 . the complements of tbe

parallelogram ML ; where+ 1 AX .

**fore**AG is equalt also to RF : therefore the fourrectangles AG , MP , PL , RF , are equal to one another , and so are quadruple of

one of ...

Side 82

1 .

passes through the centre is the greatest . Again , because EB is equal to EC ,

and FE common to the triangles BEF , CEF , the two sides FE , EB are equal to

the two FE ...

1 .

**fore**FE , EA , that is , FA is greater than FB , therefore the line which BApasses through the centre is the greatest . Again , because EB is equal to EC ,

and FE common to the triangles BEF , CEF , the two sides FE , EB are equal to

the two FE ...

Side 170

... and EF common , the two sides DE , EF are equal to the two GE , EF , each to

each ; and the base DF is equal to the base GF ; there* 8 . 1 .

is equal * to the angle GEF , and the other angles to the other angles which are ...

... and EF common , the two sides DE , EF are equal to the two GE , EF , each to

each ; and the base DF is equal to the base GF ; there* 8 . 1 .

**fore**the angle DEFis equal * to the angle GEF , and the other angles to the other angles which are ...

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Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Ingen forhåndsvisning tilgjengelig - 2018 |

Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD alternate angle ABC angle ACB angle BAC antecedent base base BC bisected Book called centre circle circle ABC circumference common consequent Const demonstrated describe diameter difference divided double draw drawn equal angles equiangular equilateral equimultiples exterior angle extremity fall fore four Geometry given straight line greater half Hence inscribed join less Let ABC logarithm magnitudes manner measure meet multiple parallel parallelogram pass perpendicular PROB produced PROP proportion proposition proved radius reason rectangle contained rectilineal figure remaining remaining angle right angles segment sides similar sine square square of AC taken tangent term THEOR third touches the circle triangle ABC wherefore whole

### Populære avsnitt

Side 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 105 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Side 65 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 70 - 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 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 172 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.

Side 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.