## A companion to Euclid: being a help to the understanding and remembering of the first four books. With a set of improved figures, and an original demonstration of the proposition called in Euclid the twelfth axiom, by a graduate |

### Inni boken

Side 65

The angles in the same

the Demonstration to Case 1st , In which the

= 2 BAD , that similarly / BFD = 2 Z BED , that : : Z BAD = BED . mi aj ni Steps of ...

The angles in the same

**segment**of a circle are equal to one another . Steps ofthe Demonstration to Case 1st , In which the

**segment**is > O . 1 . Prove that _ BFD= 2 BAD , that similarly / BFD = 2 Z BED , that : : Z BAD = BED . mi aj ni Steps of ...

Side 67

On the same straight D line , and on the same side of it , there cannot be two

similar

coinciding with each other , and prove , on that supposition , 1 . that one

must ...

On the same straight D line , and on the same side of it , there cannot be two

similar

**segments**of circles not coinciding ... and the same side of it , withoutcoinciding with each other , and prove , on that supposition , 1 . that one

**segment**must ...

Side 68

A

. To prove Case 1st , in which _ ABD = _ BAD , show that DA , DB , DC = each

other ; and : . a o described with centre d and one of these lines as distance , will

...

A

**segment**of a circle being given , to describe the circle of which it is the**segment**. To prove Case 1st , in which _ ABD = _ BAD , show that DA , DB , DC = each

other ; and : . a o described with centre d and one of these lines as distance , will

...

Side 72

That < in

ABC is a right 2 , . . the Z ARC < right Z . Steps of the Demonstration to Part 3rd ,

That _ in a

...

That < in

**segment**> 1 o is < right Ze is proved by showing that since Z BAC of AABC is a right 2 , . . the Z ARC < right Z . Steps of the Demonstration to Part 3rd ,

That _ in a

**segment**< } o is > right L . 1 . Prove that ZS ABC + ADC = 2 right Zs . 2...

Side 74

From a given circle to cut off a

given rectilineal angle . E - - - - - - - B - - - - - - - - - F Steps of the Demonstration . 1

. Prove that FBC = _ in alternate

From a given circle to cut off a

**segment**, which shall contain an angle equal to agiven rectilineal angle . E - - - - - - - B - - - - - - - - - F Steps of the Demonstration . 1

. Prove that FBC = _ in alternate

**segment**BAC , that _ in the alternate**segment**...### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

alternate angle contained angle equal applied Argument ad absurdum base bisect BOOK centre circumference coincides construction Demonstration described diameter directed divided draw Edited Engravings equal equiangular equilateral Euclid extremities fall figure given circle given point given rectilineal given straight line greater HISTORY impossible inscribe interior joins learner least less meet Nature necessary opposite parallel parallelogram pass pentagon Problem produced proof PROPOSITION Prove Prove that ZS Proved by showing READINGS rectangle contained right angles right line right Zs segment shows the supposition sides similarly square Steps straight line Suppose supposition is false Theorem touch triangle VOLUME whole whole line Young

### Populære avsnitt

Side 24 - 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, namely, either t}le sides adjacent to the equal...

Side 45 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.

Side 18 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Side 61 - From this it is manifest that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it, touches the circle...

Side 37 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 76 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 77 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on GEOMETRY.

Side 72 - If a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.

Side 27 - If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on the same side; and also the two interior angles on the same side together equal to two right angles.