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, Edlemnts of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 27
... join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the b B a 3. 1 . b 4 , 1 . C G E angle FAG common to the two triangles , AFC , AGB ...
... join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the b B a 3. 1 . b 4 , 1 . C G E angle FAG common to the two triangles , AFC , AGB ...
Página 28
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the ...
... join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the ...
Página 29
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the ver- tex of each of the triangles is without the other triangle , because AC is equal to AD , the angle ACD is equal a to the angle ADC : But the A C D ...
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the ver- tex of each of the triangles is without the other triangle , because AC is equal to AD , the angle ACD is equal a to the angle ADC : But the A C D ...
Página 31
... join DE , and upon it describe an equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to ...
... join DE , and upon it describe an equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to ...
Página 32
... join FC ; the straight line FC , drawn from the gi- ven point C , is at right angles to the given straight line AB . A D C E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF , the two sides DC , CF are equal to ...
... join FC ; the straight line FC , drawn from the gi- ven point C , is at right angles to the given straight line AB . A D C E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF , the two sides DC , CF are equal to ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism proportional proposition pyramid Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle spherical angle spherical triangle Spherical Trigonometry straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 58 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 26 - If two triangles have two sides of the one equal to two sides of the...
Página 46 - Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. s«e N. Ij'a straight line fall upon two parallel straight lines, it makes the alternate angles equal...
Página 74 - THEOR. //' a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Página 84 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight . line which is the base of the segment.
Página 411 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 118 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 54 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 49 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.