## 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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Side 48

TO describe a

TO describe a

**square**upon a given straight line . Let AB be the given straight line ; it is required to describe a**square**upon AB . a 11. 1 . From the point A draw a AC at right angles to AB ; and b 3. Side 49

1 . base BD , and between the same parallels BD , AL ; and the

1 . base BD , and between the same parallels BD , AL ; and the

**square**GB is double of the the triangle FBC , because these also are upon the same base FB , and between the same parallels FB , GC . But the doubles of equals are equal h ... Side 50

Book I. If the

Book I. If the

**square**described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other sides BA , AČ , the angle BAC is a right angle . a 11. 1 . From the point A draw a AD at right angles to AC ... Side 52

IF a straight line he divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the

IF a straight line he divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the

**square**of the whole line . A с в Let the straight line AB be divided into any wo parts in the point ... Side 53

AB ; and CE is contained by AB , BC , for BE is equal to AB ; therefore the rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the

AB ; and CE is contained by AB , BC , for BE is equal to AB ; therefore the rectangle contained by AB , AC , together with the rectangle AB , BC , is equal to the

**square**of AB . If therefore a straight line , & c . Q. E. D. PROP . III .### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1821 |

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

ABCD added altitude angle ABC angle BAC arch base Book centre circle circle ABC 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 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 17 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.

Side 35 - 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 67 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 92 - IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.

Side 26 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

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 of the whole and that part.

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 22 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Side 161 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

Side 21 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.