Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
Dentro del libro
Resultados 1-5 de 27
Página 9
... intersecting the diagonal , - the complements of the parallelogram are those subsidiary paral- lelograms through which the diagonal does not pass ; and these , with the subsidiary parallelograms through which the diagonal does pass ...
... intersecting the diagonal , - the complements of the parallelogram are those subsidiary paral- lelograms through which the diagonal does not pass ; and these , with the subsidiary parallelograms through which the diagonal does pass ...
Página 46
... and GHE . Instead of the twelfth axiom , Playfair adopts the following : - " Two straight lines which intersect one another , cannot be both parallel to the same straight line . " PROPOSITIONS . PROP . 1. - PROB . To describe 46 AXIOMS .
... and GHE . Instead of the twelfth axiom , Playfair adopts the following : - " Two straight lines which intersect one another , cannot be both parallel to the same straight line . " PROPOSITIONS . PROP . 1. - PROB . To describe 46 AXIOMS .
Página 47
... triangle , to draw arcs intersecting in the common point C , or F , and to join the points A , B , C. By an accommodation of this method , an isosceles triangle may be made : thus , -from the extremities PROP . I. - BOOK I. 47.
... triangle , to draw arcs intersecting in the common point C , or F , and to join the points A , B , C. By an accommodation of this method , an isosceles triangle may be made : thus , -from the extremities PROP . I. - BOOK I. 47.
Página 48
... intersecting in C and F , and by taking the diameter A E , D or BD , and from C and F drawing the arcs GH and IK to meet the arcs IG and KH ; the figure DGHEKID will approximate to an oval . G H C E A B F K A D 4. By drawing an ...
... intersecting in C and F , and by taking the diameter A E , D or BD , and from C and F drawing the arcs GH and IK to meet the arcs IG and KH ; the figure DGHEKID will approximate to an oval . G H C E A B F K A D 4. By drawing an ...
Página 65
... intersecting in F ; AF is the bisecting line . 2. By Prop . 9 , we show that the angles at the base of an isosceles triangle are equal ; for bisect- ing ACB by CD , CA is equal to CB , CD com- mon , and ACD equal BCD ; therefore by P. 4 ...
... intersecting in F ; AF is the bisecting line . 2. By Prop . 9 , we show that the angles at the base of an isosceles triangle are equal ; for bisect- ing ACB by CD , CA is equal to CB , CD com- mon , and ACD equal BCD ; therefore by P. 4 ...
Otras ediciones - Ver todas
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... Euclides Vista completa - 1870 |
Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
AB² ABCD AC² adjacent angles Algebra altitude angle equal angular point Arith Arithmetic ascertain Axiom bisect centre circle circumference Concl CONS construct DEANSGATE DEMONSTRATION.-P describe diagonal diameter distance drawn equal bases equilateral Euclid Euclid's Elements extremity Geometry given line given point given rectilineal given st greater hypotenuse inch interior angles intersect isosceles triangle JOHN HEYWOOD join LADC length less line be divided lines AC magnitude measure monad opposite angles opposite sides parallel parallelogram perpendicular plane Plane Geometry polygon premiss PROB produced Prop proposition Quæs radius Recap rectangle rectangle contained rectilineal angle rectilineal figure regular polygon right angles SCHOLIUM.-1 segment sides equal straight line surface trapezium twice vertical angle Wherefore
Pasajes populares
Página 93 - 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. either the sides adjacent to the equal...
Página 105 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 161 - If 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.
Página 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.
Página 93 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Página 100 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Página 180 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 18 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Página 142 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Página 44 - LET it be granted that a straight line may be drawn from any one point to any other point.