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 σελίδες |
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Σελίδα 3
... radius . Note - By the nature of its definition all radii of the same circle are equal . Ax . If the centre C of one circle is on the circumference of another circle , and a point A on the circum- ference of the first is within the ...
... radius . Note - By the nature of its definition all radii of the same circle are equal . Ax . If the centre C of one circle is on the circumference of another circle , and a point A on the circum- ference of the first is within the ...
Σελίδα 7
... radius , describe a ; and with B as centre , and BA as radius , describe a O. Suppose C one of the pts . in which the Os cut ; and join CA , CB . Since AC and AB are radii of the same O , .. AC AB . Similarly BC = BA : i . e . AC and BC ...
... radius , describe a ; and with B as centre , and BA as radius , describe a O. Suppose C one of the pts . in which the Os cut ; and join CA , CB . Since AC and AB are radii of the same O , .. AC AB . Similarly BC = BA : i . e . AC and BC ...
Σελίδα 8
... radius of the O ) = C : i . e . AD is cut off as required . Post . Let it be granted that a line , angle , or plane figure , may be conceived to be transferred , without change of magnitude , from any position to any other position ...
... radius of the O ) = C : i . e . AD is cut off as required . Post . Let it be granted that a line , angle , or plane figure , may be conceived to be transferred , without change of magnitude , from any position to any other position ...
Σελίδα 17
... radius PC describe a O , which must cut AB in two pts . , say X and Y. Join PX , PY ; and bisect XPY by PQ , meeting AB in Q. Then in As PQX , PQY , we have PX = PY , PQ common , and XPQ = YPQ ; . ' . PQX = PQY . And they are adjacent ...
... radius PC describe a O , which must cut AB in two pts . , say X and Y. Join PX , PY ; and bisect XPY by PQ , meeting AB in Q. Then in As PQX , PQY , we have PX = PY , PQ common , and XPQ = YPQ ; . ' . PQX = PQY . And they are adjacent ...
Σελίδα 24
... radius c , describe a O. " " C , " " b , 39 Then , as the vertex of the △ is at a distance c from B , ... it must lie on the O centre B. Similarly " " C. .. , if A is a pt . common to these Os , and AB , AC are joined , then ABC is the ...
... radius c , describe a O. " " C , " " b , 39 Then , as the vertex of the △ is at a distance c from B , ... it must lie on the O centre B. Similarly " " C. .. , if A is a pt . common to these Os , and AB , AC are joined , then ABC is the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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...