## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ... |

### Inni boken

Side 24

Which was to be

base of an Isosceles triangle are equal to one another ; and if the equal sides be

produced , the angles upon the other side of the base shall also be equal .

Which was to be

**demonstrated**. PROP . V. PROP . V. THEOR . The angles at thebase of an Isosceles triangle are equal to one another ; and if the equal sides be

produced , the angles upon the other side of the base shall also be equal .

Side 25

Now , since it has been

whole ACF , and the part CBG to the part BCF , the remaining angle ABC is

therefore equal to the remaining angle ACB , which are the angles at the base of

the ...

Now , since it has been

**demonstrated**, that the whole angle ABG is equal to thewhole ACF , and the part CBG to the part BCF , the remaining angle ABC is

therefore equal to the remaining angle ACB , which are the angles at the base of

the ...

Side 26

to the angle BCD ; but it has been

impossible . But if one of the vertices , as E D , be within the other triangle ACB ;

produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle

ACD ...

to the angle BCD ; but it has been

**demonstrated**to be greater than it ; which isimpossible . But if one of the vertices , as E D , be within the other triangle ACB ;

produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle

ACD ...

Side 30

Again , the angle DBA is equal to the two angles DBE , EBA ; add to each of

these equa's the angle ABC ; then will the two angles DBA , ABC be equal to the

three angles DBE , EBA , ABC ; but the angles CBE , EBD have been

Again , the angle DBA is equal to the two angles DBE , EBA ; add to each of

these equa's the angle ABC ; then will the two angles DBA , ABC be equal to the

three angles DBE , EBA , ABC ; but the angles CBE , EBD have been

**demonstrated**... Side 31

In the same manner it may be

. Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that

if two straight lines cut one another , the angles which they make at the point of ...

In the same manner it may be

**demonstrated**that the angles CEB , AED are equal. Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that

if two straight lines cut one another , the angles which they make at the point of ...

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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 - 1854 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1824 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...

Side 19 - 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 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.

Side 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 308 - 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 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 18 - 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.

Side 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.

Side 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.