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 38
Side 177
... Locus of the point satisfying that condition . * FROM GEOMETRICAL RESULTS ALREADY GIVEN , THE LOCUS OF A POINT UNDER ANY ONE OF THE FOLLOWING CONDITIONS IS AT ONCE OBVIOUS . ( a ) Condition- distance from a fixed point constant . Locus ...
... Locus of the point satisfying that condition . * FROM GEOMETRICAL RESULTS ALREADY GIVEN , THE LOCUS OF A POINT UNDER ANY ONE OF THE FOLLOWING CONDITIONS IS AT ONCE OBVIOUS . ( a ) Condition- distance from a fixed point constant . Locus ...
Side 178
... Locus the straight line bisecting , and perpendicular to , the join of the fixed points . ( e ) Condition — equidistance from two fixed lines . Locus ( 1 ) when lines are parallel , the line lying halfway between the fixed lines ; the ...
... Locus the straight line bisecting , and perpendicular to , the join of the fixed points . ( e ) Condition — equidistance from two fixed lines . Locus ( 1 ) when lines are parallel , the line lying halfway between the fixed lines ; the ...
Side 179
... Locus of the common vertex of any number of triangles , each of whose bases is fixed in magnitude and position , and the sum of whose areas is constant . E 1o , take the case of 2 As PAB , PCD , on fixed bases AB , CD , and such that A ...
... Locus of the common vertex of any number of triangles , each of whose bases is fixed in magnitude and position , and the sum of whose areas is constant . E 1o , take the case of 2 As PAB , PCD , on fixed bases AB , CD , and such that A ...
Side 180
... Loci . 1. If two circles touch ( externally or internally ) any line through their point of contact cuts off similar segments . 2. If two equal circles cut , and through one of the points of section any line is drawn , terminated by the ...
... Loci . 1. If two circles touch ( externally or internally ) any line through their point of contact cuts off similar segments . 2. If two equal circles cut , and through one of the points of section any line is drawn , terminated by the ...
Side 189
... such that their N. P. circles have a common point . Take the N. P. O as circumscribing the △ s formed by the joins of mid pts .; and use the converse of iii . 22 . EXAMPLES OF Loci . NOTE - In each of the BOOK iii . 189.
... such that their N. P. circles have a common point . Take the N. P. O as circumscribing the △ s formed by the joins of mid pts .; and use the converse of iii . 22 . EXAMPLES OF Loci . NOTE - In each of the BOOK iii . 189.
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...