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 48
Pagina 4
... proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; now , things which are equal to the same thing are equal to one another ( Axiom 1 ) ; therefore CA is equal to CB ; wherefore CA , AB , CB , are equal to ...
... proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; now , things which are equal to the same thing are equal to one another ( Axiom 1 ) ; therefore CA is equal to CB ; wherefore CA , AB , CB , are equal to ...
Pagina 6
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore , the triangles BFC , CGB are equal ( I. 4 ) , and their remaining angles ...
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore , the triangles BFC , CGB are equal ( I. 4 ) , and their remaining angles ...
Pagina 7
... proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore , the angles at the base , & c . Q. E. D. COR . Hence , every equilateral triangle is also equiangular . PROP . VI ...
... proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore , the angles at the base , & c . Q. E. D. COR . Hence , every equilateral triangle is also equiangular . PROP . VI ...
Pagina 8
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other needs no demonstration . Therefore , upon the same base , and on the same side of it , there cannot ...
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other needs no demonstration . Therefore , upon the same base , and on the same side of it , there cannot ...
Pagina 19
... is impossible ( Ax . 11 ) . The angles AGH , GHD there- fore are not unequal , that is , they are equal to one another . C G H F B Now , the angle EGB is equal to AGH * See Notes . ( I. 15 ) ; and AGH has been proved BOOK FIRST . 19.
... is impossible ( Ax . 11 ) . The angles AGH , GHD there- fore are not unequal , that is , they are equal to one another . C G H F B Now , the angle EGB is equal to AGH * See Notes . ( I. 15 ) ; and AGH has been proved BOOK FIRST . 19.
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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