## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

### Inni boken

Resultat 1-5 av 13

Side 25

greater than the

two right ... Let ABC be a triangle , of which A the side AC is greater than the side

AB ; the

greater than the

**angles ABC**, ACB ; but ACD , ACB are together equal ( 13. 1. ) totwo right ... Let ABC be a triangle , of which A the side AC is greater than the side

AB ; the

**angle ABC**, is also greater than the angle BCA . D Because AC is ... Side 102

it is required to inscribe in the cirele

DEF . Draw ( 17. 3. ) the straight line GAH touching the circle in the point A , and

at the point A , in the straight line AH , make ( 23 . 1. ) the

...

it is required to inscribe in the cirele

**ABC**a triangle equiangular to the triangleDEF . Draw ( 17. 3. ) the straight line GAH touching the circle in the point A , and

at the point A , in the straight line AH , make ( 23 . 1. ) the

**angle**HAC equal to the...

Side 297

4 , book 1. the angle BAD is equal to the angle DCB , and ABD to BDC ; and

therefore also the angle ADC is equal to the

equal to the opposite Рp 1 BOOK I. 297 NOTES . the words er evSelas, that is, in

a .

4 , book 1. the angle BAD is equal to the angle DCB , and ABD to BDC ; and

therefore also the angle ADC is equal to the

**angle ABC**. And if the angle BAD beequal to the opposite Рp 1 BOOK I. 297 NOTES . the words er evSelas, that is, in

a .

Side 398

If a triangle has one of its angles which is not a right angle given , and if the sides

about another angle have a given ratio to one another ; the triangle is given in

species . Let the triangle ABC have one of its

If a triangle has one of its angles which is not a right angle given , and if the sides

about another angle have a given ratio to one another ; the triangle is given in

species . Let the triangle ABC have one of its

**angles ABC**a given but not a right ... Side 424

PROP . LXXIV . If a triangle have a given obtuse

of the side which subtends the obtuse

which contain it , shall have a given ratio to the triangle . Let the triangle

have a ...

PROP . LXXIV . If a triangle have a given obtuse

**angle**; the excess of the squareof the side which subtends the obtuse

**angle**, above the squares of the sideswhich contain it , shall have a given ratio to the triangle . Let the triangle

**ABC**have a ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - 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 49 - 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 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.