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 60
Side 6
... square quad . quadrilateral rems . remaining And a few more similar obvious verbal contractions . Note - The symbol = is used solely as an equivalent for the words ' is equal to ' ; and means only that the sum total of all that is ...
... square quad . quadrilateral rems . remaining And a few more similar obvious verbal contractions . Note - The symbol = is used solely as an equivalent for the words ' is equal to ' ; and means only that the sum total of all that is ...
Side 44
... rectilineal figure : that is the possibility of finding a square equal in area to a given rectilineal figure . The remaining steps are given in i . 44 and 45 , and ii . 14 . Def . If any point is taken on the diagonal 44 EUCLID.
... rectilineal figure : that is the possibility of finding a square equal in area to a given rectilineal figure . The remaining steps are given in i . 44 and 45 , and ii . 14 . Def . If any point is taken on the diagonal 44 EUCLID.
Side 50
... square . Note - From the mode of construction of a square it follows that— 1o , if straight lines are equal the squares on them are equal ; 2o , if two squares are equal , any side of one is equal to any side of the other . Def . If a ...
... square . Note - From the mode of construction of a square it follows that— 1o , if straight lines are equal the squares on them are equal ; 2o , if two squares are equal , any side of one is equal to any side of the other . Def . If a ...
Side 51
... a polygon . Def . If a polygon has all its sides equal ' it is said to be equi- lateral . Def . If a polygon has all its angles equal it is said to be equi- angular . Proposition 48 . THEOREM - If the square on one E 2 BOOK i . 51.
... a polygon . Def . If a polygon has all its sides equal ' it is said to be equi- lateral . Def . If a polygon has all its angles equal it is said to be equi- angular . Proposition 48 . THEOREM - If the square on one E 2 BOOK i . 51.
Side 52
... square on one side of a triangle is equal to the sum of the squares on the other two sides , the angle contained by the latter two sides is a right angle . A B X Z Let ABC be a △ such that sq . on AB sq . on BC + sq . on AC . Take a st ...
... square on one side of a triangle is equal to the sum of the squares on the other two sides , the angle contained by the latter two sides is a right angle . A B X Z Let ABC be a △ such that sq . on AB sq . on BC + sq . on AC . Take a st ...
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...