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 10
... demonstrated , and not assumed ; and therefore , though this were a true Proposition , it ought to have been demonstrated . But , indeed , this Proposi- tion , which makes the 10th Definition of the 11th Book , is not true universally ...
... demonstrated , and not assumed ; and therefore , though this were a true Proposition , it ought to have been demonstrated . But , indeed , this Proposi- tion , which makes the 10th Definition of the 11th Book , is not true universally ...
Σελίδα 11
... demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be pro- duced , the angles upon the other side of the base shall be equal . Let ABC be an Isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle are equal to one another ; and if the equal sides be pro- duced , the angles upon the other side of the base shall be equal . Let ABC be an Isosceles ...
Σελίδα 11
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
Σελίδα 11
... BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . C F a 5. 1 . But if one of 10 THE ELEMENTS.
... BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . C F a 5. 1 . But if one of 10 THE ELEMENTS.
Σελίδα 13
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC ...
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC ...
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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.