## 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 : to this Edition are Also Annexed, Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 100

Side 8

A D / B С E 1 6 N. B. “ When several angles are at one point B , any one of " them is expressed by three letters ... upon the other line : Thus the angle which is contained by the straight lines AB , CB is named the

A D / B С E 1 6 N. B. “ When several angles are at one point B , any one of " them is expressed by three letters ... upon the other line : Thus the angle which is contained by the straight lines AB , CB is named the

**angle ABC**, or CBA ... Side 15

1 A B to DE , and A C to D F ; A and the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the

1 A B to DE , and A C to D F ; A and the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the

**triangle ABC**to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be ... Side 16

1 А equal to AC , and let the straight lines AB , AC be produced to D and E , the

1 А equal to AC , and let the straight lines AB , AC be produced to D and E , the

**angle ABC**shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. Side 24

If one side of a

If one side of a

**triangle**be produced , the exterior**angle**is greater than either of the interior opposite**angles**. ' 1 Let**ABC**be a**triangle**, and let its side BC be produced to D , the exterior**angle**ACD is greater than either of the ... Side 25

greater than the

greater than the

**angles ABC**, ACB ; but ACD , ACB are together equal ( 13. 1. ) to two right angles ... 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 .### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1810 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained 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 radius reason rectangle rectangle contained 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 11 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.

Side 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 55 - 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 53 - 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 of the line between the points of section, is equal to the square of half the line.

Side 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.

Side 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.