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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 93.
Σελίδα v
... Book v , including so much only as is necessary to render valid the proofs of Book vi : 4o , Addenda at the end of each Book , arising out of its principles , in which are given- ( a ) All the most obvious Corollaries to the ...
... Book v , including so much only as is necessary to render valid the proofs of Book vi : 4o , Addenda at the end of each Book , arising out of its principles , in which are given- ( a ) All the most obvious Corollaries to the ...
Σελίδα vii
... Book i , one in Book ii , and four in Book vi , were omitted ; because these Pro- positions are neither necessary links in the chain of proof , nor of intrinsic geometrical value . Those omitted in Books i and ii are now inserted in an ...
... Book i , one in Book ii , and four in Book vi , were omitted ; because these Pro- positions are neither necessary links in the chain of proof , nor of intrinsic geometrical value . Those omitted in Books i and ii are now inserted in an ...
Σελίδα viii
... Book vi is usually named without the parts of Book v needed in its proofs . Thus the learner finds that while an iron logic is insisted on in the first four books - so that the omission of no link in the chain of proof ( how simple ...
... Book vi is usually named without the parts of Book v needed in its proofs . Thus the learner finds that while an iron logic is insisted on in the first four books - so that the omission of no link in the chain of proof ( how simple ...
Σελίδα ix
... Books, with Numerous Additional Propositions and Exercises Euclid Randal Charles John Nixon. write out for successive ... book there will be observed a studious avoidance of crowding . Geometry arranged on the plan of ' herrings in a ...
... Books, with Numerous Additional Propositions and Exercises Euclid Randal Charles John Nixon. write out for successive ... book there will be observed a studious avoidance of crowding . Geometry arranged on the plan of ' herrings in a ...
Σελίδα xiii
... BOOK iv . Addenda to iv . Corollaries Additional Theorems Exercises . Problems depending on i 99 " " པ " " 99 " " པ i , ii i - iii i - iv • 207 208-217 218-220 221-223 221-224 221-225 221-228 BOOK v . Addenda to v . BOOK vi .
... BOOK iv . Addenda to iv . Corollaries Additional Theorems Exercises . Problems depending on i 99 " " པ " " 99 " " པ i , ii i - iii i - iv • 207 208-217 218-220 221-223 221-224 221-225 221-228 BOOK v . Addenda to v . BOOK vi .
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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...