## 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 TrigonometryBell & Bradfute, 1804 - 440 páginas |

### Dentro del libro

Resultados 1-5 de 57

Página 11

... angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . Now ,

... angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG . Now ,

**fince**it has been demonstrated , that the whole angle ABG is equal to the whole Book I. whole ACF , and the part CBG to OF GEOMETRY . 21. Página 31

... GHD are greater than two right angles . Therefore ,

... GHD are greater than two right angles . Therefore ,

**fince**KL and CD are not parallel , and do not meet towards Land D , they will meet if produced towards K and C. PROP . 1 Book I. 1 : S PROP . XXX . THEOR OF GEOMETRY . 31. Página 41

...

...

**fince**they are upon equal bases BE , EC , and between the D same parallels BC , AG ; BEC therefore the triangle ABC is double of the triangle AEC . And the parallelogram FECG is likewife double e of the triangle AEC , because it is up ... Página 55

... (

... (

**fince**CK = CB2 , and HF = AC2 ) , AB2 + CB2 = D F E 2AB.BC + AC2 . Wherefore , if a straight line , & c . Q. E. D. Otherwise , " Because AB = AC2 + BC2 + 2AC.BC , adding BC2 to 4. 2 . both , AB2 + BC2 = AC2 + 2BC2 + 2AC.BC. But BC2 + AC ... Página 57

...

...

**fince**" the square of CD is quadruple of the square of CB , the " square of any line is quadruple of the square of half that " line . " Otherwife : i " Because AD is divided any how in Ca , ADAC2 + a 4.2 . 2 CD2 + 2CD.AC . But CD = 2CB ...### Otras ediciones - Ver todas

Elements of Geometry: Containing the First Six Books of Euclid, with a ... Formerly Chairman Department of Immunology John Playfair Sin vista previa disponible - 2015 |

### Términos y frases comunes

ABC is equal ABCD alfo alſo altitude angle ABC angle ACB angle BAC arch bafe baſe baſe BC becauſe becauſe the angle biſected Book cafe cauſe centre circle ABC circumference co-fine cof BC cylinder demonſtrated deſcribed diameter draw drawn equal angles equiangular equilateral polygon equimultiples Euclid exterior angle fame ratio fame reaſon fides fince firſt folid fore given ſtraight line greater inſcribed interfect join leſs Let ABC line BC magnitudes oppoſite parallel parallelepipeds parallelogram paſs paſſes perpendicular polygon priſm proportionals propoſition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle ſame ſame manner ſame plane ſecond ſegment ſemicircle ſhall ſhewn ſide ſolid ſpace ſphere ſpherical triangle ſquare ſtand ſuch ſum ſuppoſed tangent THEOR theſe thoſe touches the circle triangle ABC uſe wherefore

### Pasajes populares

Página 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...

Página 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.

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

Página 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...

Página 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.

Página 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...

Página 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...

Página 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.

Página 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...

Página 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.