First Steps in Geometry: A Series of Hints for the Solution of Geometrical Problems with Notes on Euclid, Useful Working Propositions and Many ExamplesLongmans, Green, and Company, 1887 - 180 páginas |
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Página 24
... distance A B , he describes the circles B FE , A G D , then E B and A D , the diameters of these equal circles , are severally double of A B. 2 In constructing the figure , proceed thus : -Take A D equal to A E , and join D E ; then ...
... distance A B , he describes the circles B FE , A G D , then E B and A D , the diameters of these equal circles , are severally double of A B. 2 In constructing the figure , proceed thus : -Take A D equal to A E , and join D E ; then ...
Página 30
... he dealt with . Draw first the quadrilateral ABCD ( Fig . 14 ) , and from some assumed point , P , draw PA , PB , PC and PD , Then we have to inquire how to shift P so as to lessen the sum of the distances 30 GEOMETRICAL PROBLEMS .
... he dealt with . Draw first the quadrilateral ABCD ( Fig . 14 ) , and from some assumed point , P , draw PA , PB , PC and PD , Then we have to inquire how to shift P so as to lessen the sum of the distances 30 GEOMETRICAL PROBLEMS .
Página 31
... distances from the angles was diminishing . But if P be made to move along PA , as to P1 , then- since CP , is less than PC and PP , together , we are diminishing , not merely the sum of the distances from B and D , but the sum of those ...
... distances from the angles was diminishing . But if P be made to move along PA , as to P1 , then- since CP , is less than PC and PP , together , we are diminishing , not merely the sum of the distances from B and D , but the sum of those ...
Página 32
... distances , until we reach the intersection of P , B and A C ( which we here draw in ) . At this point of intersection , O , the second process has done all it can do for us . We see also that O is a fixed point within the quadrilateral ...
... distances , until we reach the intersection of P , B and A C ( which we here draw in ) . At this point of intersection , O , the second process has done all it can do for us . We see also that O is a fixed point within the quadrilateral ...
Página 33
... distances from P and Q shall be a minimum . We are supposed to know nothing of the pro- perty above mentioned . We might proceed then as follows : - Take the two points at very unequal distances from AB . Draw PD , QE perpendiculars on ...
... distances from P and Q shall be a minimum . We are supposed to know nothing of the pro- perty above mentioned . We might proceed then as follows : - Take the two points at very unequal distances from AB . Draw PD , QE perpendiculars on ...
Otras ediciones - Ver todas
First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... Richard Anthony Proctor Vista de fragmentos - 1888 |
First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... Richard Anthony Proctor Sin vista previa disponible - 2018 |
First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... Richard Anthony Proctor Sin vista previa disponible - 2013 |
Términos y frases comunes
A B C D A B is equal ABCD angle ABC angle BA angle equal base bisector bisects the angle circle diagonals equal and parallel equal angles equal sides equal to DC equal to half equal to twice Euclid exterior angles given angle given line given point given straight line greater Hence hypotenuse intersect isosceles triangle KHGE lines bisecting lines drawn locus maxima and minima obtuse opposite sides parallelogram perpendicular point F problem produced proof Prop proposition quadrilateral R. A. PROCTOR rect rectangle A C rectangle contained respects Euc rhombus right angles right-angled triangle sides A B solution square on CD squares on A C straight line A B theorems trapezium triangle ABC twice the rectangle vertex vertical angle
Pasajes populares
Página 80 - If two triangles have two sides of the one equal to two sides of the...
Página 144 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 175 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Página 136 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.