Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 30
Page 12
... evident proposition . A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for ...
... evident proposition . A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for ...
Page 14
... evident that the two lines must coincide entirely between A and B , for otherwise there would be two straight lines between A and B , which is impossible ( Ax . 11. ) . Sup- E A B D pose , however , that on being produced , these 4 ...
... evident that the two lines must coincide entirely between A and B , for otherwise there would be two straight lines between A and B , which is impossible ( Ax . 11. ) . Sup- E A B D pose , however , that on being produced , these 4 ...
Page 19
... evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . AA B Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ; and , taking AG from the ...
... evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . AA B Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ; and , taking AG from the ...
Page 27
... be equal to two right angles ( Prop . XX . ) , whereas it is less by hypothesis : hence , the lines ÌH , CD , are not parallel , and will therefore meet if sufficiently produced . Cor . It is evident that the two lines IH BOOK I. 27.
... be equal to two right angles ( Prop . XX . ) , whereas it is less by hypothesis : hence , the lines ÌH , CD , are not parallel , and will therefore meet if sufficiently produced . Cor . It is evident that the two lines IH BOOK I. 27.
Page 28
Adrien Marie Legendre Charles Davies. Cor . It is evident that the two lines IH , CD , will meet on that side of EF on which the sum of the two angles OGH , GOD , is less than two right angles . PROPOSITION XXII . THEOREM . Two straight ...
Adrien Marie Legendre Charles Davies. Cor . It is evident that the two lines IH , CD , will meet on that side of EF on which the sum of the two angles OGH , GOD , is less than two right angles . PROPOSITION XXII . THEOREM . Two straight ...
Other editions - View all
Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex