## Chauvenet's Treatise on Elementary Geometry |

### From inside the book

Results 1-5 of 83

Page 11

...

...

**theorem**employed in the demonstration of another theo- A problem is a question proposed for solution . An axiom is a ...**Theorems**, problems , axioms and postulates are all called propo- sitions . A corollary is an immediate ... Page 30

...

...

**THEOREM**. 74. The angle contained by two straight lines drawn from any point within a triangle to the extremities of one of the sides is greater than the angle contained by the other two sides of the triangle . From any point D , within ... Page 33

...

...

**THEOREM**. 86. In an isosceles triangle , the angles opposite to the equal sides are equal . Let AB and AC be the equal sides of the isosceles triangle ABC , then , the angles B and C are equal . For , let D be the middle point of BC ... Page 34

...

...

**THEOREM**. 89. If two sides of a triangle are unequal , the angles opposite to them are unequal , and the greater angle is opposite to the greater side . In the triangle ABC , let AB be greater than AC ; then , the angle ACB is greater ... Page 35

...

...

**THEOREM**. 74. The angle contained by two straight lines drawn from any point within a triangle to the extremities of one of the sides is greater than the angle contained by the other two sides of the triangle . From any point D , within ...### Other editions - View all

### 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.