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 Seiten |
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Seite 11
... fore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to ...
... fore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to ...
Seite 11
... fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than ...
... fore , because AC is equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than ...
Seite 14
... fore , two straight lines cannot have a common segment . A PROP . XII . PROB . E D B C To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight ...
... fore , two straight lines cannot have a common segment . A PROP . XII . PROB . E D B C To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight ...
Seite 21
... fore FK is equal to A : Again , because G is the centre of the c 15. Def . circle LKH , GH is equal to GK ; but GH is equal to C ; therefore also GK is equal to C ; and FG is equal to B ; there- fore the three straight lines KF , FG ...
... fore FK is equal to A : Again , because G is the centre of the c 15. Def . circle LKH , GH is equal to GK ; but GH is equal to C ; therefore also GK is equal to C ; and FG is equal to B ; there- fore the three straight lines KF , FG ...
Seite 26
... fore AB is parallel to CD . Wherefore , " if a straight line , ” & c . Q. E. D. See the notes on this propo- sition . a 13. 1 . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
... fore AB is parallel to CD . Wherefore , " if a straight line , ” & c . Q. E. D. See the notes on this propo- sition . a 13. 1 . PROP . XXIX . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Keine Leseprobe verfügbar - 2019 |
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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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 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...
Seite 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.
Seite 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...
Seite 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.