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 |
Αναζήτηση στο βιβλίο
Σελίδα 251
... two triangles are equiangular to each other , the sides which contain any one of the angles of the one , are proportional to the sides which contain that angle which is equal to it in the other ; and those sides which are opposite equal ...
... two triangles are equiangular to each other , the sides which contain any one of the angles of the one , are proportional to the sides which contain that angle which is equal to it in the other ; and those sides which are opposite equal ...
Σελίδα 253
... sides about the equal angles proportional , in such a manner that the pairs of sides ( cor- respondingly situated with respect to the equal angles ) are homo- logous terms in the ratios , are called ... two triangles have one BOOK vi . 253.
... sides about the equal angles proportional , in such a manner that the pairs of sides ( cor- respondingly situated with respect to the equal angles ) are homo- logous terms in the ratios , are called ... two triangles have one BOOK vi . 253.
Σελίδα 254
... two triangles have one angle of the one equal to one angle of the other , and the sides about these angles proportional , the triangles are similar ; and those angles which are opposite to the homologous sides are equal . A A B Â = Ô ...
... two triangles have one angle of the one equal to one angle of the other , and the sides about these angles proportional , the triangles are similar ; and those angles which are opposite to the homologous sides are equal . A A B Â = Ô ...
Σελίδα 260
... sides , forming an angle of one rectilineal figure , are said to be reciprocally proportional to two sides , forming an angle of another rectilineal figure ... proportional : ( B ) and conversely , if two parallelograms have 260 EUCLID.
... sides , forming an angle of one rectilineal figure , are said to be reciprocally proportional to two sides , forming an angle of another rectilineal figure ... proportional : ( B ) and conversely , if two parallelograms have 260 EUCLID.
Σελίδα 267
... two fixed points from a variable line , are in a fixed ratio , the line must go through a fixed point . 3. ABC is a triangle ; a parallel to BC is terminated by the sides ... proportional between the squares on them . 6. If the bisectors of ...
... two fixed points from a variable line , are in a fixed ratio , the line must go through a fixed point . 3. ABC is a triangle ; a parallel to BC is terminated by the sides ... proportional between the squares on them . 6. If the bisectors of ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD Addenda altitude base bisector bisects chord circum-circle circumf circumference circumscribed coincide collinear common concurrent concyclic corners cross-ratio cyclic quadrilateral diagonals diags diam diameter divided draw equal angles Euclid find the Locus fixed circle fixed point given circle given line given point inscribed intersection inverse Join Let ABC lines drawn meet mid point mid pt Note-The NOTE-Use opposite sides orthocentre pair parallel parallelogram pedal triangle perpendicular polygon PROBLEM-To produced Prop Proposition Proposition 13 quad radical axis radii radius ratio rect rectangle rectilineal figure regular polygon respectively right angles segments segt Similarly simr Simson's Line square straight line tang tangents THEOREM THEOREM-If triangle ABC vertical angle
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...