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 |
Inni boken
Resultat 1-5 av 30
Side 9
... conversely , if two plane figures , or lines , or angles , are equal in all respects , then either one of them can be placed on the other so that the two will entirely coincide . Def . Figures which can be made to coincide are said to ...
... conversely , if two plane figures , or lines , or angles , are equal in all respects , then either one of them can be placed on the other so that the two will entirely coincide . Def . Figures which can be made to coincide are said to ...
Side 38
... important additions to it - The diagonals of a parallelogram bisect each other ; and conversely , a quadrilateral is a parallelogram if its diagonals bisect each other . Proposition 35 . THEOREM - Parallelograms on the same base 38 EUCLID.
... important additions to it - The diagonals of a parallelogram bisect each other ; and conversely , a quadrilateral is a parallelogram if its diagonals bisect each other . Proposition 35 . THEOREM - Parallelograms on the same base 38 EUCLID.
Side 54
... conversely . ( 7 ) If a right - angled triangle is isosceles , each of its acute angles is half a right angle ; and conversely . ( 8 ) If two angles of one triangle are equal to two angles of another , the remaining pair of angles are ...
... conversely . ( 7 ) If a right - angled triangle is isosceles , each of its acute angles is half a right angle ; and conversely . ( 8 ) If two angles of one triangle are equal to two angles of another , the remaining pair of angles are ...
Side 55
... conversely . ( B ) If triangles on unequal bases are between the same parallels , then the triangle on the longer base is greater than that on the shorter base ; and conversely . i . 47. ( a ) A square is half the square on its diagonal ...
... conversely . ( B ) If triangles on unequal bases are between the same parallels , then the triangle on the longer base is greater than that on the shorter base ; and conversely . i . 47. ( a ) A square is half the square on its diagonal ...
Side 56
... conversely . ( 7 ) If a right - angled triangle is isosceles , each of its acute angles is half a right angle ; and conversely . ( 8 ) If two angles of one triangle are equal to two angles of another , the remaining pair of angles are ...
... conversely . ( 7 ) If a right - angled triangle is isosceles , each of its acute angles is half a right angle ; and conversely . ( 8 ) If two angles of one triangle are equal to two angles of another , the remaining pair of angles are ...
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...