Geometry, Old and New, Its Problems and Principles: A PaperSlawson & Pierrot, printers, 1879 - 48 sider |
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Side 6
... fact a prerequisite of further reasoning . Its sim- plest illustration is in the formation of a figure having three equal sides and three equal angles . This is done geomet- rically by revolving the given side first with one extremity ...
... fact a prerequisite of further reasoning . Its sim- plest illustration is in the formation of a figure having three equal sides and three equal angles . This is done geomet- rically by revolving the given side first with one extremity ...
Side 8
... fact of the highest antiquity , and the severity of its require- ment is one of the most remarkable features of the science . Considering that a line has neither breadth nor thickness , it might seem that to multiply one line by another ...
... fact of the highest antiquity , and the severity of its require- ment is one of the most remarkable features of the science . Considering that a line has neither breadth nor thickness , it might seem that to multiply one line by another ...
Side 10
... fact that it is the only figure which multiplied will completely cover space . It is true it may be done by square and hexagon , but these represent only two or more triangles . Any other figures would leave interstices . Now the ...
... fact that it is the only figure which multiplied will completely cover space . It is true it may be done by square and hexagon , but these represent only two or more triangles . Any other figures would leave interstices . Now the ...
Side 11
... fact the whole practical work of plane trigonometry is founded upon these propositions , and a world of thought has been bestowed upon their development and application . Again , it is all important in subsequent discussion to be able ...
... fact the whole practical work of plane trigonometry is founded upon these propositions , and a world of thought has been bestowed upon their development and application . Again , it is all important in subsequent discussion to be able ...
Side 12
... fact . " Other remarkable properties of the triangle are , that the three bisectors of its three angles meet in the same point , no matter what its shape may be , and that point is the center of an inscribed circle ; also , that the ...
... fact . " Other remarkable properties of the triangle are , that the three bisectors of its three angles meet in the same point , no matter what its shape may be , and that point is the center of an inscribed circle ; also , that the ...
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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.