## 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 |

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Resultat 1-5 av 6

Side 85

Upon the same straight line , and upon the same side of it , there cannot be two

similar

similar to the

.

Upon the same straight line , and upon the same side of it , there cannot be two

similar

**segments**of circles , not ... DA : and because the**segment**ACB A B issimilar to the

**segment**ADB , and that similar**segments**of circles contain ( 11. def.

Side 86

AB is equal to CD : therefore the straight line AB coinciding with CD , the

AEB must ( 23. 3. ) coincide with the

Wherefore similar

...

AB is equal to CD : therefore the straight line AB coinciding with CD , the

**segment**AEB must ( 23. 3. ) coincide with the

**segment**CFD , and therefore is equal to it .Wherefore similar

**segments**, & c . Q. E. D. PROP . XXV . PROB . A**SEGMENT**of...

Side 87

From the centre E , at the distance of any of the three AE , EB , EC , describe a

circle , this shall pass through the other points ; and the circle of which ABC is a

...

From the centre E , at the distance of any of the three AE , EB , EC , describe a

circle , this shall pass through the other points ; and the circle of which ABC is a

**segment**is described : and it is evident , that if the angle ABD be greater than the...

Side 91

1 In a circle , the angle in a semicircle is a right angle ; but the angle in a

greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw CA , dividing the circle into the

1 In a circle , the angle in a semicircle is a right angle ; but the angle in a

**segment**greater than a semicircle is less than a ... Let ABCD be a circle , of which the

diameter is BC , and centre E ; and draw CA , dividing the circle into the

**segments**... Side 297

... at least it cannot be explained in this place ; which makes it probable that this

definition , and that of the angle of a

semicircle , and the angles of

book ...

... at least it cannot be explained in this place ; which makes it probable that this

definition , and that of the angle of a

**segment**, and what is said of the angle of asemicircle , and the angles of

**segments**, in the 16th and 31st propositions ofbook ...

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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.