## Elements of Geometry: Containing the First Six Books of Euclid : with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added Elements of Plane and Spherical Trigonometry |

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Side 12

Ax . ) BG : But it has been shewn that BC is " equal to BG ;

Ax . ) BG : But it has been shewn that BC is " equal to BG ;

**wherefore**AL ' and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 12 ELEMENTS. Side 13

**Wherefore**, from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Side 14

coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ;

coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle EDF ;

**wherefore**also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ... Side 17

therefore , if the base BC coincides with the base EF , the sides BA , AC cannot but coincide with the sides ED , DF ;

therefore , if the base BC coincides with the base 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 ( 8. Ax . ) to it . i PROP . IX . PROB . Side 18

angle ; therefore each f the angles DCF , ECF , is a right angle . , :

angle ; therefore each f the angles DCF , ECF , is a right angle . , :

**Wherefore**, from the given point C , in t ' given straight line AB , FC has been drawn at right angles to AB . PROP . XII . PROB .### Hva folk mener - Skriv en omtale

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1836 |

Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circle ABC circumference coincide common consequently construction cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremity fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole

### Populære avsnitt

Side 51 - 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 12 - AB; but things which are equal to the same are equal to one another...

Side 80 - 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 288 - 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 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Side 81 - 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 which touches the circle, shall be equal to the angles in the alternate segments of the circle.

Side 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Side 127 - 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 23 - If, from the ends of the 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 19 - The angles which one straight line makes with another upon one side 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.