## 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 |

### Inni boken

Resultat 1-5 av 11

Side 10

IF F two triangles have two sides of the one equal to two

to each ; and have likewife the angles contained by those

another ; their bases , or third

be ...

IF F two triangles have two sides of the one equal to two

**fides**of the other , eachto each ; and have likewife the angles contained by those

**fides**equal to oneanother ; their bases , or third

**fides**, shall be equal ; and the two triangles shallbe ...

Side 15

are terminated in one extremity of the base cqual to one Book I. another , and

likewise their

therefore , if the base BC 27.1 . coincides with the base EF , the sides BA , AG

cannot ...

are terminated in one extremity of the base cqual to one Book I. another , and

likewise their

**fides**terininated in the other extremity : But this is impossible a ;therefore , if the base BC 27.1 . coincides with the base EF , the sides BA , AG

cannot ...

Side 28

Book I. the other

; and the third angle BAC to the third angle EDF . For , if AB be not equal to DE ,

one of them must be the greater . Let AB be the greater of the two , and make BG

...

Book I. the other

**fides**shall be equal , each to each , viz . AB to DE , and AC to DF; and the third angle BAC to the third angle EDF . For , if AB be not equal to DE ,

one of them must be the greater . Let AB be the greater of the two , and make BG

...

Side 71

For , if it be not , let , if pollible , G be the centre , and join GA , GD , GB : Then ,

because DA is equal to DB , and DG common to the two triangles ADG , BDG ,

the two

GA ...

For , if it be not , let , if pollible , G be the centre , and join GA , GD , GB : Then ,

because DA is equal to DB , and DG common to the two triangles ADG , BDG ,

the two

**fides**AD , DG are equal to the two BD , DG , each to each ; and the baseGA ...

Side 162

Therefore the

, about each of their angles , be proportionals , the triangles fhall be equiangular ,

and have their equal angles opposite to the homologous

Therefore the

**fides**, & c . Q. E. D. . PROP . V. THEOR . F the sides of two triangles, about each of their angles , be proportionals , the triangles fhall be equiangular ,

and have their equal angles opposite to the homologous

**fides**. le Let the ...### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

Elements of Geometry;: Containing the First Six Books of Euclid, with a ... Formerly Chairman Department of Immunology John Playfair Ingen forhåndsvisning tilgjengelig - 2016 |

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

Elements of Geometry: Containing the First Six Books of Euclid with a ... Euclid,Formerly Chairman Department of Immunology John Playfair,John Playfair Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD alſo altitude angle ABC angle BAC arch baſe becauſe biſected Book called caſe centre circle circle ABC circumference coincide common cylinder definition demonſtrated deſcribed diameter difference divided draw drawn equal equal angles equiangular Euclid extremity fall fame fides firſt folid fore four fourth given given ſtraight line greater half inſcribed join leſs Let ABC magnitudes meet multiple muſt oppoſite parallel parallelogram perpendicular plane polygon priſm produced PROP proportionals propoſition proved radius rectangle contained remaining right angles ſame ſame ratio ſecond ſegment ſhall ſides ſimilar ſin ſolid ſpherical ſquare ſtraight line ſuch ſum taken tangent THEOR theſe third thoſe touches triangle triangle ABC wherefore whole

### Populære avsnitt

Side 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 172 - 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 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

Side 84 - 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 106 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.

Side 22 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...

Side 64 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...

Side 166 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.

Side 54 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...

Side 2 - 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.