Geometry, Old and New, Its Problems and Principles: A PaperSlawson & Pierrot, printers, 1879 - 48 sider |
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Side 4
... applied by them to a great variety of propositions in the higher geometry , but is now entirely discarded . The severity of geometrical reasoning is such that it will not tolerate any imperfection in those things about which it arcs and ...
... applied by them to a great variety of propositions in the higher geometry , but is now entirely discarded . The severity of geometrical reasoning is such that it will not tolerate any imperfection in those things about which it arcs and ...
Side 17
... applied to numbers , there is always a common unit of measurement to every equation ; such is not the case in regard to the magnitudes with which geometry concerns itself . Here , certain lines and areas , as compared with each other ...
... applied to numbers , there is always a common unit of measurement to every equation ; such is not the case in regard to the magnitudes with which geometry concerns itself . Here , certain lines and areas , as compared with each other ...
Side 18
... applied successively for that purpose as a stand- ard , when it comes to the end it will either fall short or overlap , even if it be infinitesimally . And in like manner no unit that exactly divides the greater part will accurately ...
... applied successively for that purpose as a stand- ard , when it comes to the end it will either fall short or overlap , even if it be infinitesimally . And in like manner no unit that exactly divides the greater part will accurately ...
Side 38
... applied with marked success . The ancients knew nothing of any abstract notation , although they used analytic processes . With them the analytic method consisted in assuming the truth of the theorem to be proved , and then showing that ...
... applied with marked success . The ancients knew nothing of any abstract notation , although they used analytic processes . With them the analytic method consisted in assuming the truth of the theorem to be proved , and then showing that ...
Side 48
... applied to other de- partments of human thought : to law , to logic , to theology ? In the first place it may be replied that very many bran- ches of knowledge have already partaken largely of the accuracy and absoluteness of ...
... applied to other de- partments of human thought : to law , to logic , to theology ? In the first place it may be replied that very many bran- ches of knowledge have already partaken largely of the accuracy and absoluteness of ...
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Geometry, Old and New, Its Problems and Principles: A Paper Benjamin Gratz Brown Ingen forhåndsvisning tilgjengelig - 2009 |
Vanlige uttrykk og setninger
abstract Alexandria algebraic analytic ancients angle equal applied Archimedes arcs arithmetical axioms beauty becomes bisect bounded by right century chords circumference cissoid conception cone conic sections construction coördinates curve cycloid definite demonstration describe designation determination diagonal diagram diameter direction divided elements equation Euclid expression extremity fact figures bounded genius given line GRATZ BROWN hyperbola hypothenuse incommensurable infinite inscribed interior angles intersection investigation known let fall likewise line and circle line drawn lines and angles magnitudes Math mathematics matter measure method method of exhaustions mind multiple numbers parabola parallel parallelogram perpendicular plane Plato position problems properties propositions Ptolemy pure geometry quadrature ratio reasoning rectangle rectilinear figures reductio ad absurdum relations represent right angles right lines right triangle segment semicircle solid angles space square straight line surface thought three equal three sides tion trisection truth vertex volume enclosed whilst witch of Agnesi
Populære avsnitt
Side 14 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Side 19 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 10 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 17 - 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 sidef.
Side 23 - ... distance between the centres of the inscribed circle and of the circle through the middle points of sides has been proved to be exactly the difference between their radii ; and the same argument applies to any of the four circles which touch the three sides of the given triangle ; hence (5) The circle which passes through the middle points of the sides of a triangle touches the four circles which touch the three sides. This theorem was new both to Dr Hart and myself,* but I have lately learned...
Side 8 - THEOREM. 35. Of two oblique lines drawn from the same point to the same straight line, that is the greater which cuts off upon the line the greater distance from the perpendicular. Let PC be the perpendicular from P to AB, and suppose CE > CD; thenPU> PD. For, produce PC to P', making CP
Side 15 - Two triangles are similar if an angle of one equals an angle of the other and the sides including these angles are proportional.
Side 18 - Two diagonals of a regular pentagon, not drawn from a common vertex, divide each other in extreme and mean ratio.
Side 31 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Side 16 - In any triangle, if a straight line is drawn from the vertex to the middle of the base, the sum of the squares of the other two sides is equivalent to twice the square of the bisecting line, together with twice the square of half the base.