Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 sider |
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Side 24
... 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 angle FAG common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4 ...
... 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 angle FAG common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4 ...
Side 25
... join DC ; therefore , be- cause 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 ...
... join DC ; therefore , be- cause 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 ...
Side 26
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of each of the triangles is without the other trian- gle , because AC is equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : But the ...
... Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of each of the triangles is without the other trian- gle , because AC is equal to AD , the angle ACD is equal ( 5. 1. ) to the angle ADC : But the ...
Side 27
... join DE , and upon it describe ( 1. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bi- sects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides DA , AF ...
... join DE , and upon it describe ( 1. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bi- sects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two sides DA , AF ...
Side 28
... join FC ; the straight line FC , drawn from the given 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 tri- angles DCF , ECF , the two sides DC , CF are equal to ...
... join FC ; the straight line FC , drawn from the given 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 tri- angles DCF , ECF , the two sides DC , CF are equal to ...
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Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated 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 PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
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.