A Text-book of Euclid's Elements for the Use of Schools, Bok 1Macmillan, 1904 - 456 sider |
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Side 128
... rectangle is said to be contained by any two of its sides which form a right angle : for it is clear that both the form and magnitude of a rectangle are fully determined when the lengths of two such sides are given . Thus the rectangle ...
... rectangle is said to be contained by any two of its sides which form a right angle : for it is clear that both the form and magnitude of a rectangle are fully determined when the lengths of two such sides are given . Thus the rectangle ...
Side 129
... rectangle is divided into three rows , each containing four square inches , or into four columns , each containing three square inches . D Hence the whole rectangle contains 3 × 4 , or 12 , square inches . B Similarly if AB and AD contain ...
... rectangle is divided into three rows , each containing four square inches , or into four columns , each containing three square inches . D Hence the whole rectangle contains 3 × 4 , or 12 , square inches . B Similarly if AB and AD contain ...
Side 130
... rectangle contained by P , AB be equal to the sum of the rectangles contained by P , AC , by P , CD , and by P , DB . Construction . From A draw AF perp . to AB ; and make AG equal to P. Through G draw GH par1 to AB ; and through C , D ...
... rectangle contained by P , AB be equal to the sum of the rectangles contained by P , AC , by P , CD , and by P , DB . Construction . From A draw AF perp . to AB ; and make AG equal to P. Through G draw GH par1 to AB ; and through C , D ...
Side 131
... contains p units of length , and if AC , CD , DB contain a , b , c units respectively , hence the statement becomes ... rectangle as the product of the lengths of two adjacent sides , implies that those sides are commensurable , that is ...
... contains p units of length , and if AC , CD , DB contain a , b , c units respectively , hence the statement becomes ... rectangle as the product of the lengths of two adjacent sides , implies that those sides are commensurable , that is ...
Side 132
... rectangle contained by AB , AC ; for it is contained by AD , AC ; and AD = AB : also the fig . CE is the rectangle contained by AB , BC ; for it is contained by BE , BC ; and BE = AB . the sq . on AB = the sum of the rectangles contained ...
... rectangle contained by AB , AC ; for it is contained by AD , AC ; and AD = AB : also the fig . CE is the rectangle contained by AB , BC ; for it is contained by BE , BC ; and BE = AB . the sq . on AB = the sum of the rectangles contained ...
Andre utgaver - Vis alle
A Text-book of Euclid's Elements: For the Use of Schools : Parts ..., Bøker 1-6 Euclid,Henry Sinclair Hall,Frederick Haller Stevens Uten tilgangsbegrensning - 1889 |
A Text-book of Euclid's Elements for the Use of Schools. Books I ..., Bøker 1-6 Euclid,Henry Sinclair Hall,Frederick Haller Stevens Uten tilgangsbegrensning - 1898 |
A Text-book of Euclid's Elements: For the Use of Schools : Books I-VI and XI Euclid,Henry Sinclair Hall Uten tilgangsbegrensning - 1891 |
Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Populære avsnitt
Side 353 - 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 340 - 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 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 162 - 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.
Side 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Side 162 - 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...
Side 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Side 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Side 18 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.