## The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |

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Side 9

**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 . Side 10

Therefore the base BC coincides with the base EF , and is therefore equal to it .

Therefore the base BC coincides with the base EF , and is therefore equal to it .

**Wherefore**the whole triangle ABC coincides with the whole triangle DEF , and is equal to it ; and the other angles 10 EUCLID'S ELEMENTS . Side 15

EF , the sides BA , AC cannot but coincide with the sides ED , DF ;

EF , the sides BA , AC cannot but coincide with the sides ED , DF ;

**wherefore**likewise the angle BAC coincides with the angle EDF , and is equal * to it . * 8 Ax . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . Side 17

... the angle DBE is equal to the angle EBA ;

... the angle DBE is equal to the angle EBA ;

**wherefore**the angle DBE is equal to the angle CBE , the less to the greater ; which is impossible : therefore two straight lines cannot have a common segment . PROP . XII . PROB . Side 20

**Wherefore**, if at a point , & c . Q. E. D. c B E cause ' D PROP . XV . THEOR . If two straight lines cut one another , the vertical , or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1838 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1825 |

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

### Vanlige uttrykk og setninger

AC is equal altitude angle ABC angle BAC base base BC bisect Book centre circle ABCD circumference common cone contained cylinder demonstrated described diameter divided double draw EFGH equal equal angles equiangular equilateral equimultiples extremities fall fore four fourth given given straight line greater half inscribed join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram parallelopiped pass perpendicular plane polygon prisms produced PROP proportionals proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure remaining angle right angles segment sides similar solid solid angle sphere square taken THEOR third touch triangle ABC vertex wherefore whole

### Populære avsnitt

Side 173 - 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 56 - Iff 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 on the line between the points of section, is equal to the square on half the line.

Side 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Side 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Side 23 - Any two sides of a triangle are together greater than the third side.

Side 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.

Side 103 - 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 on the line which touches it.

Side 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Side 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.