Gradations in Euclid : books i. and ii., with an explanatory preface [&c.] by H. Green1858 |
Inni boken
Side 20
... all geometrical truths cannot be given by numbers , it is of great ... such points could make up a line ; and a line mathematical , having extension only in one ... two directions , length and breadth , no supposed piling up of surfaces ...
... all geometrical truths cannot be given by numbers , it is of great ... such points could make up a line ; and a line mathematical , having extension only in one ... two directions , length and breadth , no supposed piling up of surfaces ...
Side 22
... two lines which repre- sent the monad of surface , will represent the monad ... parts of a line , are themselves lines ; nay , from being visible , are ... rectangle of which the sides contain 4 and 3 linear units respectively : And ...
... two lines which repre- sent the monad of surface , will represent the monad ... parts of a line , are themselves lines ; nay , from being visible , are ... rectangle of which the sides contain 4 and 3 linear units respectively : And ...
Side 115
... so many threads in a piece of cloth . Now two pieces of cloth are equal , if in each there be found ... all of equal length , being equal to the same line or thread AB ... rectangle ; and it is therefore necessary to convert all parallelograms ...
... so many threads in a piece of cloth . Now two pieces of cloth are equal , if in each there be found ... all of equal length , being equal to the same line or thread AB ... rectangle ; and it is therefore necessary to convert all parallelograms ...
Side 129
... 2. When a parallelogram is drawn on a straight line , it is said to be applied to that line . USE AND APPLICATION . - This proposition contains a kind of Geometrical Division . The whole area of one figure , as C , or BF , being given ...
... 2. When a parallelogram is drawn on a straight line , it is said to be applied to that line . USE AND APPLICATION . - This proposition contains a kind of Geometrical Division . The whole area of one figure , as C , or BF , being given ...
Side 153
... all the parts , together with double the rectangle under every distinct pair of parts . Let AB = k + y + z ; then Å B2 = k2 + y2 + z2 + 2 ( k • y + y • z + k • z ) . Take a number 12 = 6 + 4 + 2 ; then 12 × 12 = ( 6 × 6 ) + ( 4 × 4 ) + ( 2 ...
... all the parts , together with double the rectangle under every distinct pair of parts . Let AB = k + y + z ; then Å B2 = k2 + y2 + z2 + 2 ( k • y + y • z + k • z ) . Take a number 12 = 6 + 4 + 2 ; then 12 × 12 = ( 6 × 6 ) + ( 4 × 4 ) + ( 2 ...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... Euclides Uten tilgangsbegrensning - 1870 |
Gradations in Euclid: Books I. and II., with an Explanatory Preface [&C.] by ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 41 - A segment of a circle, is the figure contained by a straight line and the circumference which it cuts off.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 44 - LET it be granted that a straight line may be drawn from any one point to any other point.