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 TrigonometryMarot & Walter, 1826 - 320 pagine |
Dall'interno del libro
Risultati 1-5 di 100
Pagina 21
... 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 the ...
... 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 the ...
Pagina 22
... Join CD , and if possible let CB be equal to DB ; then , in the ease 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 ease 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 ...
Pagina 23
... join DE , and upon it describe ( 1. 1. ) 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 ...
... join DE , and upon it describe ( 1. 1. ) 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 ...
Pagina 24
... join FC ; the straight line FC , drawn from the given point C , is at right angles to the given straight line AB , A D 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 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 ...
Pagina 25
... join CF , CH , CG ; the straight C A F D E G B line CH , drawn from the given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC ...
... join CF , CH , CG ; the straight C A F D E G B line CH , drawn from the given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Visualizzazione completa - 1826 |
Parole e frasi comuni
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar 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 meet multiple opposite angle parallel 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 side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Brani popolari
Pagina 125 - 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.
Pagina 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Pagina 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Pagina 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Pagina 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Pagina 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Pagina 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Pagina 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Pagina 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Pagina 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.