## 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 36

Side 18

But if one of the veriices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; thereE

But if one of the veriices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; thereE

**fore**, because AC is equal to A : D in the F triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. Side 38

**fore**the triangle ABC is equal ( 4. 1. ) to the triangle BCD , and the diameter BC divides the parallelogram ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR . PARALLELOGRAMS upon the same base , and between the same parallels ... Side 42

parallel to EF : there- A F

parallel to EF : there- A F

**fore**FECG is a parallelogram : and because BE is equal to EC , the triangle ABE is likewise equal ( 38.1 . ) to the triangle AEC , since D they are upon equal bases BE , EC , and between the same parallels BC ... Side 56

... and so are quadruple of one of them CK : again , because CB is equal to BD , and that BD is equal ( Cor . 4. 2. ) to BK , that is , to CG ; andCB equal to C B GK , that ( Cor . 4. 2. ) is , to GP ; there . A D

... and so are quadruple of one of them CK : again , because CB is equal to BD , and that BD is equal ( Cor . 4. 2. ) to BK , that is , to CG ; andCB equal to C B GK , that ( Cor . 4. 2. ) is , to GP ; there . A D

**fore**CG is equal to GP ... Side 58

... EFD are less than two right angles : but straight lines which with another straight line make the interior angles upon the same side less than two right angles do meet ( 2. Ax . ) if produced far enough : there .

... EFD are less than two right angles : but straight lines which with another straight line make the interior angles upon the same side less than two right angles do meet ( 2. Ax . ) if produced far enough : there .

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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.