## 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 16

**Wherefore**from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given straight lines to cut off a part equal to the less . a % . Side 17

**Wherefore**the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ... Side 25

**Wherefore**, if at a point , & c . ... DEB , these also are together equalato tworight angles ; D and CEA , AED have been demonstrated to be equal to two right angles ;**wherefore**the angles CEA , AED are equal to the angles AED , DEB . Side 33

1 . angle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ;

1 . angle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ;

**wherefore**... Side 44

But the parallelogram ABCD is doubleb of the triangle ABC , because the diameter AC divides it into two equal parts ;

But the parallelogram ABCD is doubleb of the triangle ABC , because the diameter AC divides it into two equal parts ;

**wherefore**ABCD is also double of the B triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII .### 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

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### 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.