## 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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Resultat 1-5 av 7

Side 32

BC be bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the

angle ACD ) , is greater than the

PROP . XVII . THEOR . Any two angles of a triangle are together less than two ...

BC be bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the

angle ACD ) , is greater than the

**angle ABC**. Therefore , if one side , & c . Q. E. D.PROP . XVII . THEOR . Any two angles of a triangle are together less than two ...

Side 95

AG , make the angle GAB equalto the angleDFE , and join G BC . Therefore ,

because А H HAG touches the circle ABC and AC is drawn from the point of

contact , the angle D HAC is equal ( 32. 3. ) to the

segment of ...

AG , make the angle GAB equalto the angleDFE , and join G BC . Therefore ,

because А H HAG touches the circle ABC and AC is drawn from the point of

contact , the angle D HAC is equal ( 32. 3. ) to the

**angle ABC**in the alternatesegment of ...

Side 130

D the angle FEG equal to the

wherefore the remaining angle BAC is equal to E the remaining angle EGF ( 32.1

. ) , and the

D the angle FEG equal to the

**angle ABC**, and the angle EFG eA. qual to BCA ;wherefore the remaining angle BAC is equal to E the remaining angle EGF ( 32.1

. ) , and the

**triangle ABC**is therefore equiangular to the triangle GEF ; and ... Side 145

... GF are parallels , the angle ADC is equal ( 29. 1. ) to the angle AGF : for the

same reason , because BC , EF are parallels , the

angle AEF : and each of the angles BCD , EFG is equal to the opposite angle

DAB ( 34.

... GF are parallels , the angle ADC is equal ( 29. 1. ) to the angle AGF : for the

same reason , because BC , EF are parallels , the

**angle ABC**is equal to theangle AEF : and each of the angles BCD , EFG is equal to the opposite angle

DAB ( 34.

Side 152

the

part of the whole circumference of the same circle : Wherefore the

**angle**BGC , have been taken any equimultiples whatever , viz . the arch BL , andthe

**angle**BGL ; and of the arch EF ... of the circle**ABC**is equal to the remainingpart of the whole circumference of the same circle : Wherefore the

**angle**BXC is ...### Hva folk mener - Skriv en omtale

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Elements of Geometry: Containing the First Six Books of Euc, With a ... Formerly Chairman Department of Immunology John Playfair,John Playfair Ingen forhåndsvisning tilgjengelig - 2017 |

### 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 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 56 - 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 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 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Side 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...

Side 130 - 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 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...

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 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.