The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's DataBell & Bradfute, 1835 - 513 σελίδες |
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Σελίδα 19
... shown that it is not equal to AB : therefore AC is greater than AB . Wherefore , angle , " & c . Q. E. D. the greater PROP . XX . THEOR . Any two sides of a triangle are together greater See N. than the third side . Let ABC be a ...
... shown that it is not equal to AB : therefore AC is greater than AB . Wherefore , angle , " & c . Q. E. D. the greater PROP . XX . THEOR . Any two sides of a triangle are together greater See N. than the third side . Let ABC be a ...
Σελίδα 23
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , " if two triangles , " & c . Q. E. D. PROP . XXVI . THEOR . If two triangles have two angles of one equal to two angles of the other ...
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , " if two triangles , " & c . Q. E. D. PROP . XXVI . THEOR . If two triangles have two angles of one equal to two angles of the other ...
Σελίδα 27
... shown that the angle C AGK is equal to the angle GHF ; therefore also AGK is a equal to GKD ; and they are E- a 29. 1 . G B H F K D alternate angles ; therefore AB is parallel to CD . Where- b 27. 1 . fore , " straight lines , " & c ...
... shown that the angle C AGK is equal to the angle GHF ; therefore also AGK is a equal to GKD ; and they are E- a 29. 1 . G B H F K D alternate angles ; therefore AB is parallel to CD . Where- b 27. 1 . fore , " straight lines , " & c ...
Σελίδα 28
... shown to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles c 13. 1 ...
... shown to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles c 13. 1 ...
Σελίδα 30
... shown to be equal to it . Therefore , " straight lines , " & c . Q. E. D. c 27. 1 . a 29. 1 . b 26. 1 . PROP . XXXIV . THEOR . The opposite sides and angles of a parallelogram are equal to one another , and its diameter bisects it ...
... shown to be equal to it . Therefore , " straight lines , " & c . Q. E. D. c 27. 1 . a 29. 1 . b 26. 1 . PROP . XXXIV . THEOR . The opposite sides and angles of a parallelogram are equal to one another , and its diameter bisects it ...
Άλλες εκδόσεις - Προβολή όλων
The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABC circumference cone cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 95 - 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 153 - 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 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 11 - 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.
Σελίδα 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 26 - 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.
Σελίδα 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.