Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of ProjectionBaldwin and Cradock, 1830 - 272 Seiten |
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Seite vi
... parallel to the same straight line . " The converse part of Prop . 14 , viz . that " parallel straight lines are at right angles to the same straight line , " will then be demonstrated as follows : - Let A B be parallel to CD , and from ...
... parallel to the same straight line . " The converse part of Prop . 14 , viz . that " parallel straight lines are at right angles to the same straight line , " will then be demonstrated as follows : - Let A B be parallel to CD , and from ...
Seite 11
... parallel : and , conversely , parallel straight lines are at right angles to the same straight line ; that is , if a straight line be drawn through the two at right angles to one of them , it shall be at right angles to the other ...
... parallel : and , conversely , parallel straight lines are at right angles to the same straight line ; that is , if a straight line be drawn through the two at right angles to one of them , it shall be at right angles to the other ...
Seite 12
... parallel : and , conversely , if two parallel straight lines be cut by the same straight line , they shall make equal angles with it towards the same parts . Let the straight lines A B , CD make equal angles BEG , DFG , with the same ...
... parallel : and , conversely , if two parallel straight lines be cut by the same straight line , they shall make equal angles with it towards the same parts . Let the straight lines A B , CD make equal angles BEG , DFG , with the same ...
Seite 13
... parallel to CD , L K is at right angles also to AB ( 14. ) . And , because , in the right - angled triangles H EL , H FK , the hypotenuse HE , and adjacent angle EHL of the one , are equal to the hypo- tenuse HF , and adjacent angle FHK ...
... parallel to CD , L K is at right angles also to AB ( 14. ) . And , because , in the right - angled triangles H EL , H FK , the hypotenuse HE , and adjacent angle EHL of the one , are equal to the hypo- tenuse HF , and adjacent angle FHK ...
Seite 14
... parallel to the sides of the other , or perpendicular to the sides of the other , in the same order , the two angles.shall be equal . Let AB C , DEF be two angles in the same plane , having the sides AB , BC of the one M parallel to the ...
... parallel to the sides of the other , or perpendicular to the sides of the other , in the same order , the two angles.shall be equal . Let AB C , DEF be two angles in the same plane , having the sides AB , BC of the one M parallel to the ...
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Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton Keine Leseprobe verfügbar - 2023 |
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Häufige Begriffe und Wortgruppen
A B C a² b² ABCD altitude asymptote axes axis base bisected centre chord circle circumference circumscribed co-ordinates common section conic section contained convex surface curve cylinder describe diameter difference dihedral angle distance divided draw drawn ellipse equal angles equation frustum given line given point given straight line gles greater hence hyperbola hypotenuse inscribed intersection join Latus Rectum less likewise locus magnitudes meet parabola parallel parallelogram parallelopiped pass pendicular perimeter perpendicular perspective projection pole prism produced projection PROP pyramid radii radius ratio rectangle rectangular rectilineal figure regular polygon right angles Scholium segment similar solid angles solid content sphere spherical angle spherical arc spherical triangle square tangent tion touch triangle ABC vertex vertical y₁
Beliebte Passagen
Seite 196 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 64 - 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 20 - In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles ; and upon BC, one of the sides containing it, let fall the perpendicular...
Seite 10 - 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 189 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Seite 1 - 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 84 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Seite 78 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Seite 79 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Seite 264 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.