## 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

Resultat 1-5 av 28

Side 31

If one side of a triangle be produced , the

the interior , and opposite angles . Let ABC be a triangle , and let its side BC be

produced to D , the

opposite ...

If one side of a triangle be produced , the

**exterior**angle is greater than cither ofthe interior , and opposite angles . Let ABC be a triangle , and let its side BC be

produced to D , the

**exterior**angle ACD is greater than either of the interioropposite ...

Side 32

Produce BC to D ; and be- . cause ACD is the

ACD is greater ( 16. 1. ) than the interior and opposite angle ABC ; to each of

these add the angle ACB ; therefore the angles ACD , ACB are greater than the ...

Produce BC to D ; and be- . cause ACD is the

**exterior**angle of the triangle ABC ,ACD is greater ( 16. 1. ) than the interior and opposite angle ABC ; to each of

these add the angle ACB ; therefore the angles ACD , ACB are greater than the ...

Side 34

Again , because the

interior and opposite angle , the

than CED ; for the same reason , the

greater ...

Again , because the

**exterior**angle of a triangle ( 16. 1. ) is greater than theinterior and opposite angle , the

**exterior**angle BDC of the triangle CDE is greaterthan CED ; for the same reason , the

**exterior**angle CEB of the triangle ABE isgreater ...

Side 38

... to the angle EFD ; but EFD is equal to the angle BCA ; therefore also the angle

BHA is equal to the angle BCA , that is , the

AHC is equal to its interior and opposite angle BCA : which is im . possible ( 16. 1

. ) ...

... to the angle EFD ; but EFD is equal to the angle BCA ; therefore also the angle

BHA is equal to the angle BCA , that is , the

**exterior**angle BHA of the triangleAHC is equal to its interior and opposite angle BCA : which is im . possible ( 16. 1

. ) ...

Side 39

its

; but it is also equal to it , which is impossible ; therefore , AB А E B and CD being

produced , do not meet towards B , G D. In like manner it may be demonstrated ...

its

**exterior**angle AEF is greater ( 16. 1. ) than the interior and opposite angle EFG; but it is also equal to it , which is impossible ; therefore , AB А E B and CD being

produced , do not meet towards B , G D. In like manner it may be demonstrated ...

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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 - 1837 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

### 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.