Euclid Revised: Containing the Essentials of the Elements of Plane Geometry as Given by Euclid in His First Six Books, with Numerous Additional Propositions and ExercisesClarendon Press, 1890 - 400 sider |
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Side vi
... greater brevity , clearness , and simplicity . strictly in accordance with Euclid's order and methods . making these changes the Editor has not been guided by à priori They are all In considerations of what might , could , would , or vi ...
... greater brevity , clearness , and simplicity . strictly in accordance with Euclid's order and methods . making these changes the Editor has not been guided by à priori They are all In considerations of what might , could , would , or vi ...
Side viii
... greater than the third , surely it is necessary to prove ex æquali , componendo , and alter- nando . Every teacher admits the absurdity of the prevailing system ; but the truth is that what does not ' pay ' in examinations is not , and ...
... greater than the third , surely it is necessary to prove ex æquali , componendo , and alter- nando . Every teacher admits the absurdity of the prevailing system ; but the truth is that what does not ' pay ' in examinations is not , and ...
Side ix
... greater benefit by having to hunt up the references themselves . It is suggested that writing in the references ( in pencil ) should form part of the business of preparation . Various Propositions , distinguished as A , B , C , etc ...
... greater benefit by having to hunt up the references themselves . It is suggested that writing in the references ( in pencil ) should form part of the business of preparation . Various Propositions , distinguished as A , B , C , etc ...
Side xi
... greater , but to less appreciation of the logic — that the more argument is focused the clearer and stronger impression it produces — that , in fine , brevity is the soul of reason- ing , as it is of wit . The Editor was brought to this ...
... greater , but to less appreciation of the logic — that the more argument is focused the clearer and stronger impression it produces — that , in fine , brevity is the soul of reason- ing , as it is of wit . The Editor was brought to this ...
Side xii
... greater freedom , than some examination programmes have hitherto permitted , is directed to the recommendation passed by the Cambridge Board of Mathematical Studies ( May 10 , 1887 ) that " the actual proofs of propositions as given in ...
... greater freedom , than some examination programmes have hitherto permitted , is directed to the recommendation passed by the Cambridge Board of Mathematical Studies ( May 10 , 1887 ) that " the actual proofs of propositions as given in ...
Vanlige uttrykk og setninger
ABCD Addenda altitude base bisector bisects centre of similitude chord circum-circle circumf circumference coincide collinear concyclic corners cross-ratio cyclic quadrilateral diag diagonals diam diameter divided draw drawn equal angles equiang Euclid find the Locus fixed circle fixed line fixed point given circle given line given point harmonic conjugates inscribed intersection inverse Join Let ABC magnitudes meet mid point mid pt Note-The NOTE-Use opposite sides pair parallel parallelogram pedal triangle perpendicular polygon PROBLEM-To produced Prop Proposition Proposition 13 Ptolemy's Theorem quad radical axis radii radius ratio rect rectangle rectilineal figure respectively right angles segments segt Similarly simr Simson's Line square straight line tang tangents THEOREM THEOREM-If touch triangle ABC variable
Populære avsnitt
Side 251 - 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.
Side 29 - 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.
Side 150 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Side 91 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Side 82 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 37 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Side 44 - 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.
Side 84 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 22 - Any two sides of a triangle are together greater than the third side.
Side 87 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...