Chauvenet's Treatise on Elementary Geometry |
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Page 11
... scholium is a remark upon one or more propositions , pointing out their use , their connection , their limitation , or their extension . An hypothesis is a supposition , made either in the enun- ciation of a proposition , or in the ...
... scholium is a remark upon one or more propositions , pointing out their use , their connection , their limitation , or their extension . An hypothesis is a supposition , made either in the enun- ciation of a proposition , or in the ...
Page 16
... Scholium . A straight line revolving from the position OA around to the position OB describes the two right angles AOC and COB ; hence OA and OB , regarded as two different lines having opposite directions ( 4 ) , are frequently said to ...
... Scholium . A straight line revolving from the position OA around to the position OB describes the two right angles AOC and COB ; hence OA and OB , regarded as two different lines having opposite directions ( 4 ) , are frequently said to ...
Page 21
... Scholium . The preceding demonstration applies when the en- veloping line is a curve , or any species of line whatever . PROPOSITION IX . - THEOREM . 35. Of two oblique lines drawn from the same point to the same straight line , that is ...
... Scholium . The preceding demonstration applies when the en- veloping line is a curve , or any species of line whatever . PROPOSITION IX . - THEOREM . 35. Of two oblique lines drawn from the same point to the same straight line , that is ...
Page 22
... Scholium . Two points are sufficient to determine a straight line ( 3 ) ; hence any two points each of which is equally distant from the extremities of a straight line determine the perpendicular at the middle of the line . Thus if P ...
... Scholium . Two points are sufficient to determine a straight line ( 3 ) ; hence any two points each of which is equally distant from the extremities of a straight line determine the perpendicular at the middle of the line . Thus if P ...
Page 25
... Scholium . When the secant line is oblique to the parallels , there are formed four equal acute angles and four equal obtuse angles , and each acute angle is the supplement of each obtuse angle . But if any one of the eight angles is a ...
... Scholium . When the secant line is oblique to the parallels , there are formed four equal acute angles and four equal obtuse angles , and each acute angle is the supplement of each obtuse angle . But if any one of the eight angles is a ...
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Common terms and phrases
ABCD adjacent angles allel angle AOB angle BAC angles are equal apothem arc AC BC² bisector bisects called centre chord circum circumference coincide Corollary Definition diagonals diameter dicular distance divided draw equal angles equally distant exterior angle ference figure four right angles geometry given angle given point given straight line greater hence homologous sides hypotenuse inscribed inscribed angle intercepted arcs less Let ABC measured by one-half middle point number of sides oblique lines one-half the arc opposite sides parallel to BC parallelogram pendicular perimeter perpen perpendicular points of intersection produced proportion PROPOSITION quadrilateral quantities radii radius ratio rectangle regular polygon rhombus right angles right triangles Scholium secant line segment semi-circumference side AC sides are equal square straight line drawn symmetrical with respect tangent theorem triangle ABC triangles are equal vertex
Popular passages
Page 201 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 31 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP
Page 201 - Words, Facts, and Phrases : A Dictionary of Curious, Quaint, and Out-of-the-Way Matters. By ELIEZER EDWARDS.
Page 120 - Any side of a spherical triangle is less than the sum of the other two.
Page 81 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 92 - Every point in the bisector of an angle is equally distant from the sides of the angle...
Page 58 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.