Hopefully your continued exposure to chemical selected names and terms is beginning to bear fruit.
So let us carry on with unravelling the history of the subject.
The ancient Greeks thought there were four elements, Earth, Water Air and Fire and that all substances were made up from these.
In fact they used a different word and the word element came into English from the Latin elementum.
Furthermore the concept was very vague in detail and one Greek in particular (Democritus) asked the important question.
"What happens if you cut a substance in half, then in half again and in half again and so on ?"
He proposed that you would eventually reach a stage where the substance became indivisible and called this piece atomos from where we get the English word atom.
This situation continued until the late 17 hundreds when Dalton revived the twin concepts and included the new question
"If you can cut substances apart, how can you put them together ?"
In his words he described atoms as
"All atoms of the same element are alike, globular and all of the same magnitude, but atoms of different elements have different weights."
Thus moving atoms from substances to elements and making the distinction.
It should be noted that 'weights' were not measured in pounds and ounces or kilogrammes.
Hydrogen was give the weight exactly 1 unit and other elements were measured as multiples (including decimal fractions) of this.
These weights were called atomic weights.
This was a great step forward but it did not explain how or why atoms could be combined in 'fixed proportions' to form substances they could split up.
Atoms could not be split up i.e. were indivisible.
These insights plus the growing list of elements enabled the first versions of the periodic table to be drawn up.
But they were wrong because they placed elements in order of increasing atomic weight, which led to inconsistencies in the chemical properties compared to their placement in 'the table'.
The table is called periodic because these properties occur at regular spacing when the elements are placed in the proper order.
They had not yet addressed the second question "How can you put them togerther?"
Then in 1869 Hofmann, then working in england, coined the English word 'quantivalence'.
He introduced the concept of Valency or the combining power of atoms and your next equation from chemical mathematics.
Atomic weight = Equivalent weight x Valency.
This ushered in the third era in the History of Chemistry and led to a new idea - that of the molecule.
At that stage, they still though atoms were 'indivisible' they did not know about electrons, protons and neutrons - that comes in the fourth period up to the present day and was largely invetigated by Physicists.
So they quickly determined that oxygen has 2 'hooks' , carbon has 4 'hooks' and nitrogen has '3 hooks' and hydrogen has 1 hook.
These hooks were also quickly translated into the ubiquitous chemical stick diagrams we still use today.
Here is the diagram for 'ethane' where you can quickly see that each carbon is linked by 4 sticks or hooks and each hydrogen is linked by 1 stickk or hook.
This is the 'molecule' of pure ethane.