The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 σελίδες |
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Αποτελέσματα 6 - 10 από τα 18.
Σελίδα 206
... prisms of the same alti- tude , the base of one of which is a parallelogram , and that of the other a triangle ; if the ... prism half of GO . Therefore ( I. ax . 7. ) the prisms are equal . Wherefore , if there be two triangular prisms ...
... prisms of the same alti- tude , the base of one of which is a parallelogram , and that of the other a triangle ; if the ... prism half of GO . Therefore ( I. ax . 7. ) the prisms are equal . Wherefore , if there be two triangular prisms ...
Σελίδα 210
... prisms , which together are greater than half of the whole pyramid . Let there be a pyramid of which the base is the triangle ABC , and the vertex D : the pyramid ABCD may be divided into two equal and similar triangular pyramids ...
... prisms , which together are greater than half of the whole pyramid . Let there be a pyramid of which the base is the triangle ABC , and the vertex D : the pyramid ABCD may be divided into two equal and similar triangular pyramids ...
Σελίδα 211
... prisms are equal : therefore the prism having the parallelo- gram EBFG for its base , and the straight line KH opposite to it , is equal to the prism having the triangles GFC , HKL for its bases ; for they are of the same altitude ...
... prisms are equal : therefore the prism having the parallelo- gram EBFG for its base , and the straight line KH opposite to it , is equal to the prism having the triangles GFC , HKL for its bases ; for they are of the same altitude ...
Σελίδα 212
... prism having the triangles LXC , OMN for its bases , to the prism of which the bases are the triangles RVF , STY . And because the two prisms in the pyramid ABCG are equal to one another , as also the two in the pyramid DEFH ; as the ...
... prism having the triangles LXC , OMN for its bases , to the prism of which the bases are the triangles RVF , STY . And because the two prisms in the pyramid ABCG are equal to one another , as also the two in the pyramid DEFH ; as the ...
Σελίδα 213
... prisms : these two prisms ( XII . 3. ) are greater than the half of the whole pyamid . Again , let the pyramids made by this division be in like manner divided , and so on , until the pyramids which remain undivided in DEFH , are all of ...
... prisms : these two prisms ( XII . 3. ) are greater than the half of the whole pyamid . Again , let the pyramids made by this division be in like manner divided , and so on , until the pyramids which remain undivided in DEFH , are all of ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - 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.
Σελίδα 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Σελίδα 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 40 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...