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 42
Pagina 6
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . Let ABC be an isosceles ...
Pagina 7
... Again , be- cause CB is equal to DB , the angle BDC is equal ( I. 5 ) to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . See Notes F But if one of the vertices , as D BOOK FIRST . 7.
... Again , be- cause CB is equal to DB , the angle BDC is equal ( I. 5 ) to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . See Notes F But if one of the vertices , as D BOOK FIRST . 7.
Pagina 11
... demonstrated to be equal to the same three angles ; and things that are equal to the same thing are equal ( Ax . 1 ) to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same thing are equal ( Ax . 1 ) to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ...
Pagina 12
... demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & e . Q. E. D , A B D COR . 1. From this it is manifest , that , if two straight lines cut one another , the angles which they make at the point of ...
... demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & e . Q. E. D , A B D COR . 1. From this it is manifest , that , if two straight lines cut one another , the angles which they make at the point of ...
Pagina 13
... demonstrated , that BAC , ACB , as also , CAB , ABC are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . A A B THEOR . The greater side of every triangle has the greater angle opposite to it . A ...
... demonstrated , that BAC , ACB , as also , CAB , ABC are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . A A B THEOR . The greater side of every triangle has the greater angle opposite to it . A ...
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Elements of Geometry; Containing the First Six Books of Euclid, With Two ... John 1748-1819 Playfair Anteprima non disponibile - 2021 |
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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