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 TrignonometryBell & Bradfute, 1875 - 257 pagine |
Dall'interno del libro
Risultati 1-5 di 93
Pagina 7
... 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 ...
Pagina 9
... join DE , and upon it describe ( I. 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 com- mon to the two triangles DAF , EAF ; the two sides DA , AF are ...
... join DE , and upon it describe ( I. 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 com- mon to the two triangles DAF , EAF ; the two sides DA , AF are ...
Pagina 10
... join CF , CH , CG ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . D Because FH is equal to HG , and HC is common to the two triangles FHC , GHC , the two sides FH , HC are equal ...
... join CF , CH , CG ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . D Because FH is equal to HG , and HC is common to the two triangles FHC , GHC , the two sides FH , HC are equal ...
Pagina 12
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( I. 15 ) to the angle CEF ...
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( I. 15 ) to the angle CEF ...
Pagina 13
... join BD ; and because ADB is the exterior angle of the triangle BDC , it is greater ( I. 16 ) than the interior opposite angle DCB ; but ADB is equal ( I. 5 ) to ABD , be- cause the side AB is equal to the side AD ; therefore the angle ...
... join BD ; and because ADB is the exterior angle of the triangle BDC , it is greater ( I. 16 ) than the interior opposite angle DCB ; but ADB is equal ( I. 5 ) to ABD , be- cause the side AB is equal to the side AD ; therefore the angle ...
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Parole e frasi comuni
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore given circle given point given straight line hypotenuse inscribed less Let ABC Let the straight meet multiple opposite angle parallel parallelogram perpendicular plane polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles segment semicircle similar sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC straight line drawn tangent THEOR third three straight lines touches the circle triangle ABC triangle DEF wherefore